The Knights Templar, possibly the most famous of the "Big Three" orders (the others being the Hospitaller and Teutonic), was disbanded by Papal decree in 1312, although by that point the leadership of the order had been already been imprisoned for five years by Philip IV of France on charges of heresy in a massive round-up of Templars on Friday 13th of October, 1307. The build up to these events had taken place over the last few decades.
By the turn of the 14th century, the Mamluks finally captured the island-fortress of Arwad from the Templars, their last remaining bastion in the Holy Land, forcing the Templars to relocate their operations to the island of Cyprus. Essentially, this was the end of the crusader presence in the Holy Land, leaving the Templars without a cause. Their brothers in the other holy orders, such as the Hospitallers and Teutons had alternative missions to turn to, such as holding the island of Rhodes from the Muslims, or carving out a monastic state in the Baltics. The Templars had no such activity to point to as a reason for the continued support of Christendom; the loss of this support would not have been catastrophic, had the Templars not been accumulating resentment at an increasing pace.
The Templars were not simply the soldiers they are often portrayed as. They were certainly a military order, and two of the three classes of Templars had military roles within the order. The eponymous Knights were primarily there to protect pilgrims, while the Sergeants, who were most often the tradesmen and artisans of the order, were also called upon to fight when the need arose. The third was the Chaplains who tended to the spiritual needs of their brothers. Some estimates put their total membership at fifteen to twenty thousand strong, with about ten percent of that number being Knights. This is a substantial amount of people to feed, clothe, and shelter, which requires resources of an equally substantial amount.
Since the early years of the order, the Knights Templar had received certain benefits from the Pope, which had accumulated both the wealth they needed to operate, as well as the resentment referred to earlier. For starters, the Templars were unable to be taxed on any of their property, they answered only to the Pope, could travel through any border at will, and did not need to abide by any local laws. During the heyday of the Crusades, with the full backing of the Papacy, the Templars benefited greatly from donations of gold, land, and businesses, which only continued to grow with time, with their network of chapter houses allowing a effective form of banking to take place; pilgrims wishing to travel across Christendom could deposit their wealth in their local chapter house, receive a receipt, travel to where they wanted to go, then hand over their receipt to the chapter house there and receive their wealth back. This was infinitely safer than making the journey carrying your wealth, and of course the Templars took a cut of the wealth they protected. So by the time Arwad fell to the Mamluks, the Templars were a vastly powerful, wealthy, international order that was subject only to Rome. With the fall of Arwad, They had also lost their primary reason for existing, and so the sharks began to gather.
The privileges the Templars enjoyed often came at the expense of local lords, who lost sources of income from donations to the Templars, lost their legal jurisdiction in those donated lands, and had to put up with heavily armed bands of warriors tramping across their territory. Still, even with the loss of Arwad, the Templars could have continued. Like the Teutons and the Hospitallers, their mission could have adapted to the new circumstances, but we will never know, because Philip the Fair then struck.
Philip IV, called the Fair not because of his just nature but rather because of his good looks, was in a spot of economic trouble. I won't go into the details, but by 1305 the French coinage was only 30% precious metal, having been debased in a failed attempt to recover the economy. Philip was also fighting wars with far too much regularity to be healthy, and wars are frightfully expensive, and so the French king was resorting to ever more villainous ways to gain wealth. After expelling Lombard merchants and seizing their property, he then did the same to the Jewish population, as well as arranging a special tithe from the church, although he handled the reintroduction of wealth into the economy so poorly that there were riots in Paris. Philip took shelter from the rioters in the Templar citadel, where the wealth of the order would have been clear.
So in September 1307 the arrest warrants went out across his kingdom, with orders to arrest any local Templars in one months time, which went off without a hitch. Notably, very few Templars escaped these arrests, suggesting that both Philip's administration was startlingly efficient, and also that the Templars were clearly not overwhelmingly popular. The Grand Master, Jacques de Molay, was attending the funeral of Philip's sister-in-law when he and sixty of his fellows were arrested. In November, Clement V dispatched the Pastoralis Praeeminentiae, which called for the immediate arrest of all Templars.
The Templars were accused of heresy and grevious sins, including homosexuality, bestiality, spitting on the cross, the worship of idols, and incorrect conduct of mass by Templar chaplains. What followed were mass tortures of Templars, leading to confessions of these charges as well as a raft of other crimes. Pope Clement V was the first Avignon Pope, essentially a French puppet, although he did attempt to rein in the tortures by demanding certain conditions of the trials, with torture only to be used when the accused would not testify either way. Since Philip remained the jailer of the Templars, he arranged for them to be tortured anyway. Still, the Templars began to adequately defend themselves, especially since many Knights were noble-born and had received some education in the law. The Grand Master, Molay, repeatedly recanted his confessions the moment he was in front of a Papal commission and away from the royal agents, only to succumb to torture when back in their custody and repeat his recantation all over again.
The resistance of the Templars was largely destroyed in 1310, after three years of trials and torture. Philip, using the previous confessions, as well as the recanted confessions, to have fifty four of the men that had been arrested alongside Molay dragged out of Paris and burnt at the stake. Less than a week later, another nine Templars were burnt thirty miles north of Paris. Philip's threat was clear as day; play along, confess your 'sins', and accept the punishment. Or die screaming. The vast majority did so, serving their sentences in prisons, but otherwise surviving. In 1312, the previous mentioned Papal edict, Vox in Excelso, was enacted, and across Christendom to repression of the Knights Templar began, although with varying levels of severity. In England, for example, Edward II dallied and pretended to fulfill the Pope's will, but largely left the Templars alone. Contrarily, in Cyprus, the Templars base, they would be involved in a standoff with the local military as well as their Hospitaller brothers, although it was largely bloodless. In France, where this had all began, the trials continued without much difficulty, after the example made by the firey deaths of sixty-three of their fellow Templars, until it came time to sentence the Grand Master in 1314. Using his previous confessions, Molay was to be sentenced to life imprisonment, but as the sentence was about to be laid down he, along with three of his surviving comrades, stood and denounced the trial as a farce. I'm going to quote a 19th century historian here, Henry Charles Lea, mainly because his account is brilliant reading:
They had been guilty, they said, not of the crimes imputed to them, but of basely betraying their Order to save their own lives. It was pure and holy; the charges were fictitious and the confessions false. Hastily the cardinals delivered them to the Prevot of Paris, and retired to deliberate on this unexpected contingency, but they were saved all trouble. When the news was carried to Philippe he was furious. A short consultation with his council only was required. The canons pronounced that a relapsed heretic was to be burned without a hearing; the facts were notorious and no formal judgment by the papal commission need be waited for. That same day, by sunset, a pile was erected on a small island in the Seine, the Ile des Juifs, near the palace garden. There de Molay, de Charney, de Gonneville, and de Peraud were slowly burned to death, refusing all offers of pardon for retraction, and bearing their torment with a composure which won for them the reputation of martyrs among the people, who reverently collected their ashes as relics.
That was effectively the end of the Templars. Survivors were either imprisoned, let off, or merged with other military orders, and their vast wealth disappeared into the purses of various lords, Philip the Fair first among them. Philip and Clement were both short-lived, though, with Clement dying suddenly within a month of Molay's burning, and Philip being mortally wounded during a hunting trip before the year was out.
Sources:
EDIT: For further details on the aftermath of the trials, the fate of the Templars in other kingdoms that I didn't mention, and the workings and future of the Hospitallers and Teutonic Knights, take a gander at /u/Rhodis' comments further down this thread.
I never realised warrior monks were a real thing! Can anyone point me in the direction of some good resources on the lives of warrior monks?
As u/Surprise_Institoris has given a great answer on the falling out of favour with the church part of your question, this answer addresses when the tradition of warrior monks died out.
The tradition of warrior monks did not fully die out in Europe until well into the early modern period. The first order of these warrior monks, normally called military orders or military religious orders, was the Knights Templar, founded around 1119 and originally intended to protect pilgrims in the East. The Knights Hospitaller were technically founded earlier, in the late eleventh century and confirmed by the Pope in 1113, but they began as a charitable order and did not militarise until after the Templars were formed. Other military orders soon followed. By 1200 there were at least five international military orders: the Templars, Hospitallers, Teutonic Knights, Knights of St Lazarus, Knights of St Thomas of Acre. More regional orders had also been formed, like the Knights of Santiago and Knights of Calatrava in Iberia. Each order shared the same main purpose, conducting holy war against non-Christians. Some, including the Teutonic, Hospitaller, St Thomas, and Lazarite orders also provided medical and charitable care.
In the following centuries more new orders were formed. The Swordbrethren were established around 1204, and marked a new development in the purpose of a military order. Instead of being directed against Muslims, the Swordbrethren were deployed against pagans. Military orders were also deployed against heretics. The Militia of the Faith of Jesus Christ, given papal consent in 1221, fought against the Albigensians (Cathars) in southern France. The orders even saw use as peacekeepers, like the Order of the Blessed Virgin Mary in 1261, which was tasked with calming the conflict between rival political factions in northern Italy. After the Fourth Crusade conquered Constantinople in 1204, a order was set up to manage a hospital there and help defend the new Latin kingdom from the Byzantines, the Order of St Sampson.
Foundations became more rare in the late medieval period. There was less interest from patrons in donating to both military and non-military monastics in the fourteenth and fifteenth centuries as other displays of piety became more popular, like chantries and collegiate churches, and the costs of foundations rose. However, new orders were still proposed, they just rarely made it off the page, like Philippe de Mezieres' Order of the Passion. The Reformation further sucked the life out of the military order, with most Protestant countries expelling the orders. Aside from an offhand proposal in Tudor Ireland in 1540, no other Protestant nation appears to have considered establishing a new military order either.
In Italy there were some new regional orders established, like the Knights of St Stephen and the Order of SS Maurice and Lazarus, both of which conducted naval campaigns like the Hospitallers but also served as political factions for their founders. However, the era of the new military order was clearly in decline. At their inception in the crusader states, the military orders were a necessity. The crusaders were chronically short of manpower and the orders provided a well-funded standing army. With the final loss of the Holy Land in 1291, the end of crusading in the Baltic and Iberia in the fifteenth century, and the development of national standing armies, the military orders began to be left without a purpose.
New orders were still proposed, and in some cases founded, as late as 1890, but these were typically the realm of eccentrics. Armies that marched only on paper, like the Order of the Christian Militia, founded in 1616 by Charles Gonzaga, titular emperor of Constantinople, with the aim of conquering Greece. The last military order that I've been able to trace was the Armed Brothers of the Sahara, established in 1890 by Cardinal Charles Lavigerie. The Armed Brothers were based in Algeria and spent two years fighting Arabic slave-traders before their dissolution in 1892.
Sources:
Alan Forey, ‘The Military Orders and Holy War against Christians in the Thirteenth Century’, The English Historical Review, Vol. 104, No. 410 (Jan., 1989).
Helen Nicholson, The Knights Hospitaller (Woodbridge, 2001).
Helen Nicholson, The Knights Templar a New History (Stroud, 2001).
Jonathan Riley-Smith, The Crusades, Christianity, and Islam (Chichester, 2008).
Desmond Seward, The Monks of War (London, 1972).
Dionysios Stathakopoulos, 'Discovering a Military Order of the Crusades: The Hospital of St. Sampson of Constantinople', Viator, Vol. 37, 2006.
Joan Williamson, ‘Philippe de Mézières and the Idea of Crusade’, in Malcolm Barber (ed.), The Military Orders: Fighting for the Faith and Caring for the Sick (Aldershot, 1994).