During the reign of the Spanish Empire, despite the appointment of various Viceroys, Captains-General, Governors, Audienca's, etc. the Spanish Crown attempted to maintain as much central control of the economies and internal functions of their colonial possessions.
This included restrictions on trade to include a mercantille system that forbade trading with non-Spanish merchants which led to a large black market for manufactured goods from countries such as France and Holland. Spain during this era had a very poor agrarian focused economy and produced very few manufactured goods. This mean high prices in the colonies due to irregular shipments as well as the black market. It was not until the mid part of the 18th Century that Spain began to relax these restrictions but by then it was too late to settle much of the resentment and frustration that had begun to arise from this.
On another part, Spain was, to put it bluntly, absolutely terrible with its money. In fact, one of the origional motivations for Spain to send Columbus to India was to allow them to gain a foothold in lucrative Far East Trade to not merely continue it's efforts of the Reconquista in North Africa, but to pay off its already existing war debts. In fact, during most of the existence of the Spanish Empire, the entire haul of the Treasure Fleets rarely met its already existing debts much less its anticipated expenditures for the year. At some points it would hold debts in excess of three times its expected income.
Spain regularly defaulted on its loans from Italian and German bankers and was regularly refinancing them in an attempt to reduce their payments. In fact, it can be argued that part of the collapse of the wealth of Italian financiers was directly related to Spains outright statements that it would simply say, "Can't pay, sorry, what can you do?" on their outstanding loans. This led to the shift of European finance away from Italian states such as Venice to German and Swiss agents.
As part of this failure to pay on the regular, or even finance itself, this would lead to cities in the Empire lacking strong defenses from raids by privateers and pirates, soldiers and civil servants to go without pay for years at a time, and a general lack of support of infrastructure and development.
This included Spain's inability to develop a professional and government controlled navy. Seriously, for much of the history of the Empire, Spains navy was built and operated by contractors, bought abroad (the first non-galleon ships of Spain were bought from France), and was regularly outdated and outfought. Because of this inability to support its navy, constant raids and attacks by other nations, mostly the English and Dutch with France playing its own part when it wasn't trying to merge with Spain...which played a part as well... Because of this lack of navy and defense in the Empire, colonists grew frustrated with what appeared to be apathy and incompetence from home.
Spain fought several long, costly, and ultimately crippling wars in Europe during it's time as an Imperial power. Unfortunately, Spain treated these as its main focus at the expense of the colonies. This not only was the constant source of Spains financial woes, but all of its political and administrative efforts. The colonists began to feel that Seville and later Madrid didn't care much about them as long as the silver kept flowing. In fact, as sources of silver in the New World would begin to go dry, it could be seen where Spains efforts at improving local government, reducing corruption, and building infrastructure changed. To Spain, their Empire was merely a way to finance their wars on the Continent. This led to no small amount of resentment by a growing number of people who were born, lived, and died, without ever seeing Spain, but were called Spaniards.
By the time Spain had begun serious internal reforms in the mid and later half of the 18th Century, it had already fallen to at best a second class European power, and had abandoned most of its Continental goals. However, the reforms could not come fast enough. It was until almost the 1780's that the inefficiant Treasure Fleets came to an end. While before that the restrictions on trade were lifted, it still wasn't enough. Enough resentment from the colonists had built up, and despite the surprising growing prosperity of the Empire, it wasn't quite reflected in the colonies as much of the silver wealth was still flowing back to Europe. With the American revolution serving as a template, many of these local populations lost their identity of being a Spaniard and being more of a "New Granadan" or "Peruvian", etc.
When France overthrew Charles IV in Spain during the Peninsular War during the Napoleonic era, many of these former colonies simply began self government in the absence of a legitimate king in their eyes. By the time of the restoration of Charles IV Ferdinand to the throne, many of these former colonies had been governing themselves independently for almost a decade and simply sought to make themselves formally independent through full revolutions. By the time Spain was in any position to begin allowing self-rule or dominion status for its possessions, they simply couldn't stop them from leaving completely (and never really would since all the way to the end, Spain wanted and needed the income from its colonies) or being taken away like Cuba and the Philippines.
In summation. By the time it crossed anyone mind, the opportunity was long gone.
For what happened during and after the Bourbon restoration, check out Thucydides post.
There are two moments we have to look at. The first wave of Hispanic American independence, 1808-1825, and the post-1837 separatist movements culminating in the Spanish American War in 1898 and resulting loss of colonies in America and Asia.
In 1808 Napoleon used disturbances in Aranjuez (a plot by supporters of the future Ferdinand VII against Minister Godoy and his father, Charles IV) as an excuse to pressure almost the entire Bourbon dynasty of Spain to come to Southern France for Napoleon (at the height of his power) to settle their differences. The military might of France combined with the fact that Portugal had already been occupied in 1807 led to the Bourbons acquiesing and traveling to Bayonne in mid-1808. Rather than 'settle' the dynastic issues they were having, Napoleon forced Ferdinand and Charles to abandon their claims on the Spanish throne, followed by his push to place his own brother, Joseph as the new king.
French troops co-opt or otherwise neutralize the traditional mechanisms of government in Spain and attempt to secure a swift and easy transition to the new Napoleonic dynasty.
This lead to the Junta (think similar to "counsel") movements in Spain and abroad. Since the sovereignty of the monarchy had fallen, the direction of the country fell back on Medieval institutions. Since these were also tainted, local governments took center stage and organized in Juntas which began directing local affairs as well as opposition to the French and the imposition of Joseph Napoleon as king.
In the Americas the Junta movement began as officially in favor of restoring Ferdinand VII ("El Deseado", or "The Desired One"). Even Hidalgo and Morelos in New Spain (Mexico), at the head of a massive indigenous peasant army were officially fighting to restore Ferdinand to the throne.
As time passed (Ferdinand wasn't restored until Napoleon's defeat in 1814) these movements evolved into full on separatism, with Venezuela declaring independence in 1811 and others following suit.
The period from 1808-1820 was one of lots of back and forth between separatists and those fighting to keep the colonies under Spanish rule. The de facto Spanish government also experienced a lot of back and forth, with events leading to the establishment of a Liberal (with a capital L) provisional Cortes in the years following 1808 and the establishment of a Liberal constitution in 1812 (this is big because previously Spain was an absolutist monarchy, barely contained by medieval privileges enjoyed by many of its peninsular possessions). Lots of creoles supported what we'd call Liberal ideas, but many were also much more conservative and wary of Liberal anti-clericalism and reformist policies. Liberalism also meant the attempt to modernize the relationship between Spain and its colonies, in a way that benefited European Spain to a greater degree (something colonials were very wary of).
Ferdinand was restored in 1814 and between that date and 1820 he pushed and almost reconquered most of his American possessions. Then, in 1820, a Liberal Spanish officer led a revolt of reinforcements intended to invade America and turned them back towards Madrid to reimpose the 1812 Constitution, which Ferdinand had set aside once he was restored to power.
This led to a crisis of Spain's remaining American possessions. Conservative (lower case c) minded creoles were aghast with the possibility of being governed by Spanish Liberals and instead began supporting conservative minded political Revolutions. The best example would be Agustin de Iturbe's creation of the Empire of Mexico in 1821. He had requested a scion of the Bourbon dynasty to be the monarch of an independent Mexico, the closest thing to a "Commonwealth" that could be envisioned within the context of Spanish political tradition at the time, but Ferdinand and the Liberals refused, leading to him crowning himself as Emperor (only to be overthrown in 1823).
Once Ferdinand was able to overthrow the Liberals and their constitution in 1823, his attempts to invade the Americas with fresh troops failed utterly, time and again throughout the rest of the 1820s.
Basically, the elites in Spain during this period were incapable of imposing their dominance of their American possessions but also unwilling to recognize the creation of a cadet branch which would have been the contemporary equivalent of a "Commonwealth".
So, Cuba and Puerto Rico remained to Spain (Haiti had invaded and conquered the future Dominican Republic and I'm not to clear on how things evolved for them during the 19th century) but the rest of its American Empire was lost.
After a period of serious absolutist reaction, known as the ominous decade, between 1823-1833, his heir Queen Isabel II, supported and was supported by the Liberal faction. Absolutist reactionaries fought this with the support of the rival claimant, Carlos, but they fail. In 1837 Spain inaugurates a new era both in the history of Spain and its governance of its colonies with a constitution which formalizes the colonial status of the ultramarine (overseas) possessions of Spain (think what England had wanted to do to its American colonies before 1776).
This ends the colonial pact with Cuban elites developed between the reformist, though absolutist, Bourbons of previous decades and local planters. Thus begins a period of increasing conflict between Spain and Cuba which leads to lots of winking support to separatists looking to unite Cuba with the US and eventually resulting in the first independence war, 1868-1878. To keep this short I'm simplifying things a bit, but the essential idea is that while the post-1878 settlement reformed certain points of colonial rule (and abolished slavery), it neither resolved the economic contradictions between Spanish merchants/policies and Cuban exporters, was insufficient in satisfying creole desires for modernization along the lines of the US, nor could it erase the blot of all the creole blood spilled during the independence war (including attrocities and arbitrary killings by Spanish voluntary militias, "Voluntarios"). Spain was also unable to satisfy the dangerous Cuban exile community in the US which successfully reorganized, financed provisions for, and sent and invasion force to renew hostilities in Cuba in 1895. Spanish attempts to quell this involved the "Reconcentracion", forcing all Cubans to move to towns whether or not they could support themselves there (to keep them from supporting rebels in the countryside) and leading to the deaths of around 100,000 civilians through starvation. In essence, too little, too late. Cuban identity was evolving, resentment of Spain was strong, and honestly (as Raymond Carr points out), Spain was unlikely to be able to provide the markets and modernizing impulse that Cubans would have needed to see in order to convince them to remain within the monarchy.
Bibliography:
Miguel Artola: La Espana de Fernando VII
Raymond Carr: Modern Spain, 1808-1975.
Manuel Moreno Fraginals: Cuba/Espana Espana/Cuba: Una Historia Comun.
Tulio Halperin: The Contemporary History of Latin America.
Follow up question, did the downfall of the Spanish empire influence Britain's decision-making when forming the Commonwealth? Or was it the independence of the US that primarily influenced their choices?