The western empire was gradually defeated militarily by the Germanic tribes, technically. If you consider him the last emperor, Romulus Augustulus was simply deposed by Odoacer and from then on, in theory, the western emperor’s seat was simply vacant. Claimants for the seat would come and go for millennia.
I guess the question is why nobody cared enough to fill the seat. The eastern emperor probably at first considered himself to be western and eastern emperor by default, and I guess that situation lasted until sometime around Justinian, who re-conquered much of the west and Africa (bringing the Eastern Empire to its greatest post-5th century extent). That was the last time the eastern empire exerted effective control over most of the west.
Here is one possible answer why that stopped: in the mid-6th century, Europe had a massive plague outbreak, which probably killed tens of millions of people. This crippled the Eastern Empire so much that it never really recovered territorially, and made it easier pickings for Muslims in the next century. By the time the empire sort of recovered militarily, several centuries had gone by and the Germanic kingships that established in the former western empire were powerful in their own right. The book Justinian’s Flea is a good read for some extensive background about this period.