The Romans never controlled Arabia or a good portion of the Middle East (Persia, and all points east)... A world where the Arabs are completely untogether and can't defeat either the Romans OR the Sassanids would probably lead to the outcome you're speaking of.
Arab conquests or not, the Turks are still going to start arriving in the area between 900-1000. Without Islam, I wonder if they might become Christian? It's possible they could achieve a peaceful unity with the Roman Empire if they convert to Orthodox Christianity -- although if that's the case modern Turkey might not deserve the name at all.
As I see it, the Romans' logical goals were to defend Greece/Anatolia first, the Levant second, and North Africa third. Remember that right at the time the Arabs came the Romans and Sassanids were recovering from a brutal war with each other. Maybe if you get rid of this war, then the Arabs would be less lucky.
Remember, also, that most of the people east of Persia who converted did so (relatively, for the day and age) peacefully -- so even if Islam's western advance is halted, I still think it would be a major world religion (assuming the Arabs still defeat the Sassanids).
If the Romans hold onto the Levant, I'd say that might butterfly away the Crusades to a certain extent -- but there's still a lot of Christian European infighting, one of the reasons for the Crusades. Possibly, the Catholics would decide to "liberate" Jerusalem from the heretical Orthodox Christians, leading to an alternate Crusade against the Eastern Roman Empire -- the Orthodox/Catholic split was still recent enough that I don't know if this would happen. However, I think that'd be an interesting TL.
If the Latin Catholics invaded the Orthodox Levant, then the Muslims (including the Turks? Possibly) would step in, leading to a massive three-way war for the Holy Land. Okay, I actually really like this idea. It may be time to start my first TL.
One consequence of this might actually be a shortened lifespan for the Roman Empire... The Latins' sack of Constantinople in 1204 was something the Romans never recovered from; imagine if the Catholics had been intending to fight the Romans from the very beginning.