The problem is ALL empires eventually fall, none have lasted for ever. And the Roman empire didn't fall with the barbarian invasions of the 5th century, only the Western half did. The Eastern Roman empire (which we call Byzantine) lasted for another thousand years. But ok, lets speculate....
IF the Western Roman empire had survived the 5th century, then it would have changed over time. The West and East halves of the empire (officaly split in 396 AD) would have evolved separatley; Latin in the West and Greek in the East. Christianity, already the state religion by 320 AD, would still have grown in the medieval period. The Franks who took over Gaul would either have been absorbed by the Western empire or would have stayed in Germany. If absorbed, there may well have been a succession of Frankish emperors; so the 'Holy Roman Empire' may have been centred on Italy, or a new capital (like Constantinople) may have been built in Gaul/France.
What would have happened with the Arab invasions of the 7th century....I don't know.
What would have happened with the Viking invasions of the 9th century....I don't know.
Would feudalism have taken hold in the Western empire....I don't know.
But I know one thing....there would have been a lot of civil wars in the west! That's one of the disadvantages of emperors compaired to an established monarchy; ANYONE can be emperor.
So I very much doubt that the Western empire could have lasted much longer than than the Eastern empire did. Far too politically unstable.