Mesopotamia as Traianus had seized it was unsustainable. Traianus essentially occupied all of the territory that didn't put up a fight, leaving several hostile fortresses in his rear, while completely ignoring the Iranian plateau, where the claimants to the Pahlavan throne fought amongst themselves. He reached the Gulf, then turned around to try to finish the job, but by then the civil war had been resolved, Roman armies were overstretched, the Jews started rebelling (as they were wont to do) and Traianus himself died attempting to capture Hatra, one of the major fortified cities that threatened Roman control in Mesopotamia.
Hadrianus' decision to pull back to the Euphrates was both intelligent from a military standpoint - abandoning terrain that he was likely to lose anyway - and statesmanlike. Rome didn't have the logistical infrastructure in place for a sustained Mesopotamian war until the second half of the second century, perhaps not even until the reign of Septimius Severus. (The "perhaps" arises both from my personal lack of knowledge and from my conviction that historians who do know about this stuff don't know precisely when these reforms occurred, either.) It might perhaps have been wiser for Hadrianus to demand a small buffer zone on the far side of the Euphrates - the sort of territory Rome held after Septimius' campaigns - but Roman control there was as tenuous as it was anywhere else, and the local populace had not been acclimatized to Rome as they would be later.
