Why did the Spanish Empire have difficulty subduing and then maintaining control of the Netherlands?

The Spanish empire faced three big problems in the 80 years war; geography, finance, and foreign military intervention.

Break out a map and you may notice something a little funny, Spain does not border the Netherlands. Spain used two methods to get troops and money to the Netherlands, sea and land.

The land route was called the Spanish Road and was by far the more important of the two methods. Spain possessed territory in northern Italy, and the Holy Roman Empire was ostensibly under the Habsburg dynasty. The ideal route was that soldiers would be recruited in Spain, then shipped to northern Italy for garrison duty. After a little bit of time acclimating to the military life in garrison duty, these soldiers would be ordered to the Netherlands. The exact routes traveled along the eastern border of France and the western border of the Holy Roman Empire, and through several small, independent political territories.

Since the HRE was ostensibly Habsburg, access via its territory would seem an easy issue. However, the HRE was incredibly politically fragmented and what should have been guaranteed access to the Netherlands was actually more like something out of a Katy Perry song, hot and cold. Specifically, the Electors of Palatine and the dukes of Zweibrucken (both part of the HRE) were incredibly hostile to the Habsburgs. These guys routinely harassed Spanish soldiers, confiscated their weapons, stole their money, and in general were majors pains in the ass. Their activity made the use of the Rhine to move troops into the Netherlands a haphazard affair for the Spanish. Because of this, the Spanish usually went a little more west and passed through Lorraine. Spain's access to the various territories needed to move troops waxed and waned over the years as various powers decided to intervene, or were distracted by other concerns and unable to impeded Spain.

Movement by sea was never a reliable option for Spain. In 1568, the English decided to end their alliance with Spain. With England, France, and the Netherlands hostile to Spain, movement by sea was impossible. Almost every attempt by Spain to move troops or money by boat to the Netherlands ended in disaster.

I think it's a bit of an understatement to say that Spain's finances were as messy and confusing as their land routes. You have to remember that imperial Spain was more akin to a feudal state than to what we think of as a modern nation, or even the Roman empire. As an essentially feudal lord, the king of Spain did not have powers of general taxation. Instead, the war was considered a personal matter of the king and so he was personally responsible for raising the funds necessary. He possessed the sole political right to allow the raising of troops, but actually funding them was an entirely different matter. The the king of Spain could raise money in four different ways. The first was in rents and tolls on the use of his land. The second was through special project, such as the extraction of wealth from the New World. The third was by taking out loans. And the fourth was by convincing wealthy Spanish nobles to become personally involved and contribute their own wealth and credit to the affair. Going into even a little detail on these methods would require a huge amount of writing, so I'm only going to touch briefly on number three, loans. In order to actually move money to the Netherlands to pay soldiers, Spain could either ship the required gold and silver themselves, or they could take out short term loans called "asientos". The asiento was basically an agreement by a banker to provide money in the Netherlands in exchange for being paid money in Spain. However, Spain was never able to pay back the asientos in full, and frequently defaulted. This wiped out Spanish bankers and forced the king to go international in order to obtain loans. In the end, Spain destroyed their creditors one by one, and as their access to credit plummeted, so did Spain's ability to finance their army.

Foreign military intervention was the last major factor that effected Spain's ability to wage war in the Netherlands. Simply put, the 80 years' war was not the only thing on Spain's plate. Spain was the principle power behind checking Ottoman influence in the Mediterranean, as Venice had long ago lost the ability to stand against the Ottomans unaided. The Dutch frequently reached out to the Ottomans and encouraged them to create problems for the Spanish, thus diverting men and money that would otherwise fund Spain's war in the Netherlands. France was another problem. During the first half of the 80 years' war, France was consumed by their own internal problems. However, this did not stop them from interfering whenever possible with movement along the Spanish Road. However, once France got past their wars of religion, they began a unified effort to cripple the Spanish Empire. One problem was that since France and Spain were both catholic, they were supposed to be allies. However, the secular lust for power, overrode any loyalties due to religion. The French contributed heavily to the protestants in the 30 years' war in an attempt to interfere with Spain. France eventually abandoned all pretense and directly fielded armies against the Habsburgs in the HRE and the Netherlands.

In short, Spain faced conflict in every direction and they lacked the internal organization or foreign alliance necessary to solve their problems one at a time. They simply had to much to do at one time and not enough resources to do it. Coupled with the incredibly awkward geography impeding their access to the Netherlands, and it's a testament to Spanish obstinence that they managed to fight on as long as they did.

Sources:

"The Army of Flanders and the Spanish Road: 1567-1659" by Geoffry Parker. This is my primary resource since the book is literally about the question you asked. It's a bit dry in places, and it assumes that the reader is fairly familiar with European politics and geography of that time period, but it has lots of good details.

"The 30 Years' War" by C.V Wedgwood. The final 30 years of the 80 Years' War overlapped with the 30 Years' War, and while the two wars started as different wars, they essentially ended as the same war. Wedgwood does an excellent job of describing the general moods and feelings of the different political players as time went on.