In 2007, Derek Kennet published an article in which he carefully cataloged all the archaeological materials from the Gulf region, and noted that almost none of it dated from the Sasanian period. This would indicate that the period was an economic low point, rather than a height. This was a significant challenge to the received wisdom, though it has begun winning acceptance. In an article that came out in the 2011 Proceedings of the Seminar for Arabian Studies, I reexamined the written evidence and found that it did not, in fact, support the "Sasanian prosperity" school of thought as it was once believed to do.
Much of the debate on this topic relates to Oman. The argument that Sasanian Oman was exceptionally prosperous derives ultimately from a 1973 article by J.C. Wilkinson. My concern with Wilkinson is that his use of the evidence seems to have been led by his expected conclusions and paradigms of the day, and that more natural interpretations would portray a more ambiguous picture. For example, Wilkinson was inclined to take the official Sasanian historiography at face value, whereas today we are more inclined to see it as an expression of ideology and propaganda. A key part of this, following in the wake of Parvaneh Pourshariati's Decline and Fall of the Sasanian Empire, is that Sasanian rulers tended to be internally weak and dependent on their relationships with powerful nobles. This has implications for the extent to which Sasanian policies were implemented throughout the realm, and for the fact that Wilkinson emphasizes the fact that the 6th-century ruler Khusrau I pursued economic development throughout his realm.
One Omani source says that 4000 of the Sasanian cavalry called Asawirah were stationed in Oman under the Sasanians. Leaving aside whether that was true, Wilkinson interpreted them as landowners, even though none of the sources he cites actually say that. This is not to say that they weren't, only that there is no evidence on the point. In fact, in both Oman and what is now eastern Saudi Arabia, I am inclined to differentiate between qualitative and quantitative evidence, and assess relative economic prosperity solely on the basis of the latter. Whether archaeological or the written evidence of urban foundations, such quantitative evidence does not show a great deal of Sasanian investment in Arabia, regardless of accounts that testify to some sort of presence. During most of their four centuries, the Sasanians probably saw Arabia as a frontier to defend against rather than a region from which to extract resources.
However, the matter is far from settled. In particular, Oman has been far less explored archaeologically than some other areas, and the coast facing the Gulf of Oman could prove an exception. Portrayals of an Arabian prospering like never before under Sasanian rule, however, need to be taken with a grain of salt.