Eh, a lot of reasons.
1) Political stability. While war between the Byzantine and Sassanid Empires had devastated both sides, Byzantines had had an uninterrupted continuity of government. Sassanid Empire meanwhile had been left with rulers with no political legitimacy, leading to a series of civil wars - or rather one massive civil war lasting for 14 years. These devastated the empire and its military power in the years between the last Byzantine-Sassanid war and the Arab onslaught.
2) Geography. While both empires had some exposed areas (Syria etc. in general) and some very defensible areas (Anatolia, Iran), Byzantine Empire also had the Mediterranean - it was essentially a naval power, and used this advantage against the Arabs. Constantinople was also very removed from the front line, and could simply not be taken without a fleet. Persia had none of these advantages - it was a land power, and its capital was largely landlocked and exposed in the flat areas. And while Byzantine center of power was in Anatolia (though economic centre was Egypt), Persian center of power was in Iraq - which was lost early on.
3) Political and military organization. Byzantine Empire was a centralized power, allowing it to quickly reform its military. Byzantine armies had been severely weakened by their defeats, but not destroyed: thus they were settled across the Empire, and soldiers were given plots of land from which they drew sustinence. This provided a very tough defensive force, akin to the National Guard. Persian military however was feudal in nature, and political instability meant that many nobles didn't really care to fight for the Emperor. This included the Seven Parthian Clans, that were the foundation of the Empire's military power. Essentially, Persians could only really rely on the Shah's household troops. And Iran - which did have geography to resist the Arabs - was politically in no position to do so. Political instability was far worse there - Iran was basically impossible to control and so Persian emperors had to rely on a system of personal alliances and local nobility to do so. So long as they were able to do it, Persia was nearly impossible to conquer - but the war against the Byzantines had weakened the Shah's authority, and so Persians lost control of Iran just when they needed it the most. (Parallel may be drawn to how the feudalized Byzantine Empire quickly lost Anatolia against the Seljuks, though question is again more complex).
4) Strategy. This is perhaps the most important aspects - Romans were simply smarter, or perhaps luckier, ironically thanks to suffering more at the beginning. Having lost massive areas very quickly, Empire was aware that it was in no position to launch a counterattack. And most of Byzantine army had actually survived these defeats. Thus, the primary task was to organize defense, and any illusion of recovering the lost areas was lost very quickly. This also meant that Byzantines gradually shifted away from the "decisive battle" doctrine that had exemplified their early engagement with the Arabs. Persians however kept seeking a decisive battle, sending army after army to face the Arabs - until they had no armies left. And once that happened, Persian Emperor (Yazgerad III) was assassinated, and Persia broke up into numerous fiefdoms that were then captured one after another. Had they done as Byzantines had, they could have easily held onto Iran at least - but they didn't.
