The city seemed to be extremely vulnerable to Roman incursions from the north-west, being captured several times in the late Parthian and early Sasanian periods. Did any Sasanian kings try to move the capital to a more defensible location, or was Ctesiphon simply too important to the empire for other reasons?
Some great responses in this thread, so I'll just add my brief views to it.
The Sasanian frontier with Rome was highly fortified, and their defensive strategy was usually to bog the Romans down with sieges until their very formidable field forces could be assembled (McDonough 608-10), at least until they developed their professional forces in the 6th and 7th centuries (603). These fortifications also had important roles in countering banditry but could be double-edged swords in the event of rebellion (610).
As for Ctesiphon, the Sasanids had many royal cities that, like fortifications, primarily sheltered the revenue raising agricultural lands of the empire and increased royal control over the markets (611). Also important is the need for control over the Empire's western and northern frontiers, which Ctesiphon is situated near, in ensuring the loyalty of frontier troops, who usually did most of the fighting (606).
So as /u/ByzantineBasileus has stated, economic reasons must have been prominent. However, Ctesiphon may have been the capital but was one of many "royal cities" that formed the physical and moral foundations of the power of the shahanshah. Probably far more important for the prestige (and physical safety) of the shahanshah was the performance of the field army, which was often very successful but in the event of major defeat would drastically impact the king's position, or cost him his life (615). Perhaps Ctesiphon, even if it was the capital, did not have the importance to the much less centralised Sasanian empire that, for example, Rome or Constantinople did to the Romans. Ctesiphon was clearly located in a strategicially important area, and served an importance purpose as did other royal cities. Its vulnerability was unfortunate, but it was pretty heavily protected and its fate was probably less important in any war than the success of the field army in battle.
Source: Scott McDonough, Part III Military and Society in Sasanian Iran. From The Oxford Handbook of Warfare in the Classical World, Eds. Brian Campbell and Lawrence A. Tritle, Oxford University Press, New York, 2013, 601-620.
One reason could certainly be economic. Ctesiphon was in Mesopotamia, which historically had been a highly developed area. There was a great deal of industry, irrigation, trade, roads and other urban communities. It would be logical to have a capital in a region with the infrastructure to support it.
There would also have been a lot a of wealth there, and correspondingly a great amount of possible income from taxation. My own personal theory is that the best way to control this region is to actually have the main centre of government there. The region always seemed difficult to hold on to for a power based in Iran itself. It is worth noting that, after Gaugamela, Babylon and the other cities were occupied very quickly by Alexander, and there was nothing the Persians could do about it. Likewise the Safavids of Iran always had difficulty holding onto Baghdad. The Tigris and Euphrates always helped an invader coming down from the north west (which was always the main invasion route from the west).
Sources
Iran at War: 1500-1988, by Kaveh Farrokh
Sasanian Persia: The Rise and Fall of an Empire, by Touraj Daryaee
Shadows in the Desert, by Kaveh Farrokh