The idea has been raised before; and a few days ago someone resurrected this
topic about the same subject. The suggestion was dismissed out of hand. The fall of the Roman empire was not caused by one event, but a series of processes (top of my head: economical decline, continious border warfare, regular civil war) that sapped the strenght and stability of the empire. While I won't say Rome was doomed to fall, it seems unlikely that it would have managed to halt or reverse all these processes.
Anyway, the question of what would happen if the empire had never fallen can simply not be answered. It is too long ago for anything but wild speculation. The empire wouldn't have gone into stasis: the world changes and an empire has to change with that, or fall. But how it would have changed we cannot predict.