To begin with, the hardest part is perhaps making Byzantium weak enough to fall to the Arabs. Constantinople was extremely difficult to capture, further, even with conquest, I doubt with utmost certainty, Muslims will not succeed in holding it. In Iran, the Umayyad continued wars deep into Central Asia engaging the falling Gokturks and then pushing the frontier in India. Whereas, in Europe, they will have to face the invasions of Slavs, Bulgars, Magyars and the already strong Avars and Khazars. There is very little chance they hold anything west of Anatolia.
Also, it should be noted, that I find it unlikely that even if the Sassanids survive, that they won't fall to the Muslim caliphates. Eventually they will succumb, and likely, far sooner than Byzantium. Their geography simply does not lend itself to defense as much as Byzantium did and unlike Byzantium, they will not have Constantinople or vast land of Armenians, Georgians etc holding their frontiers. Infact, the best lands of Iran are near Iraq and the heartlands of Islam, making it a matter of life or death to win pitched battles on the Zagros mountains or in Khuzestan. Further, the entire Persian Gulf will be infested with Arab piracy, and to add to this, the Muslim caliphate will have venues for invasion from sea and from Qeshm into Hormuz from Oman, making it even more difficult to hold out.
As well, there is the Turks and other tribes of the steppe that will make the status of Iran very, very dangerous. Byzantium had a seperation of its two heartlands by sea limiting the effect of predatory peoples such as the Rus, Bulgars and Pechenegs keeping a lid on the amount of damage done to each region. Not to mention, Constantinople saved the empire from total ruin more times than any other capital has saved a nation. There is no way, Susa or Ectbatana will be able to hold out as Constantinople did and it is more dangerous in its location, right on the border with Islamic heartlands. Imagine though, a Turkish tribe arrives and breaks through Ferghana as the Hepthalites did, and proceed to push deep into unpopulated lands inflicting chaos; this goes on just as the Caliphate leads an invasion into Iran. It would require a ruler or general of elite calibre to win this engagement or just to keep the empire alive. Not to mention, this devastation is felt all over, unlike Byzantium which, can suffer devastation in Greece to an extent that it has little effect on Anatolia or vice versa.
Basically, in my opinion, a non Muslim Iran has no chance against the Caliphates in a long term geopolitical conflict, at least without a very lucky several decades.