Sura, or at least that area, was within the Roman province of Mesopotamia as of the reign of Septimius Severus when he conquered the area around 200CE. The province fell to the Sasanians, as you mentioned, about 50 years later.
Trajan conquered the area north of Sura about a hundred years earlier and created the original province of Mesopotamia; however, his successor Hadrian relinquished Roman control of areas that far east when he became emperor. Severus reconquered the area and recreated the (now larger) province of Mesopotamia in 198CE, though it was a frequent source of conflict.
However, during the un-creatively named Crisis of the Third Century, Rome had some trouble keeping control of its empire. This crisis included several civil wars, invasions, and a single year in which six Roman emperors rose and fell. Understandably, Rome's neighbors took advantage of the situation, including the somewhat recently formed Sasanian Empire which took much of the eastern Roman provinces in the mid/late 3rd century CE.