The Sassanids in no way "allowed" their last great war with Byzantium to go into a stalemate. The Sassanids did absolutely try to conquer the whole Empire. They sent in magistrates to govern the eastern provinces, systematically secured fortresses to ensure there were no Romans to their rear, and launched a massive force to capture Constantinople that was simply beaten. Heraclius had collected the Roman field armies, which gave him an army larger than any individual Persian army, and brilliantly maneuvered them to defeat the main 3 Persian armies. He continually defeated Persian armies while raiding northern Mesopotamia and then finally launched an absolutely devastating raid on Mesopotamia and systematically tore the country apart. Panic spread and reached Ctespihon, the Persian Capital, causing the Shah, Khosrau II, to be overthrown and the new party sue for peace. Heraclius shattered the Persian army and destroyed their economic heartland, the Sassanids just got beat so badly they were willing to give up the conquered territory to make peace.