I don't think that Islam can be eliminated by military forces from Persia. It would at least survive as a local sect on the Arabic peninsula.
No, probably not, but there's also another scenario I can imagine...
The Byzantines and the Persians are more successful against the Muslims, and a large portion of the Caliphal military is destroyed. The prestige of Islam is hugely damaged, tribes began to break away, and at some point, the Muslim leadership itself gets into a series of civil wars. Islam atomizes, and by 700 the Arabian pennensula has, politically, gone back to the way it was before Islam. No one wrote down the Quran or hadith, so Muhammad has become something of a legendary figure, with different versions of his teachings circulating (though they all seem to agree that Muhammad was a strict monotheist and had nice things to say about Christ).
At this point, at least some of the different "Muslim" sects are going to start identifying themselves with Christianity, most likely the non-Chalcedonianism of Egypt and Syria. Gradually, as Coptic and Jacobite influences penetrate more into Arabia, this becomes more common (no one really knows the specifics of what Muhammad said by this time, so the idea he was really a non-Chalcedonian Christian isn't all that farfetched). Eventually, a non-Chalcedonian "Church of Arabia" forms, which regards Muhammad as a great Saint, a legendary figure who tried to bring the gospel of Christ to the heathen Arabs. Nice hagiographic writings of Muhammad's saintly life are produced, with little relation to reality. Ultimately, he's remembered as a minor historical figure in a rather peripheral part of the world.
