I'm sure we've discussed this before but what if the Syrian Christian refugee Kallinikos was captured (or killed) by the Arab forces before he is able to reach the Byzantines in Constantinople? Without it, I doubt the Byzantines would be able to defeat the Umayyad navy in the Sea of Marmara, ending all attempts to resupply the besieged defenders by sea. There's still the factor that the Arabs might be beset with starvation when winter comes though they can wait out the Byzantines until they starve to death. Another question is what happens next after Constantinople falls to the Caliphate?