A few possible reasons:

• Western Emperors of the 5th century were generally quite dismal; the very survival of the Empire up to the deposition of Romulus Augustule is almost a miracle, which would not have occurred save for the exceptional abilities of a few generals (we should perhaps say “a few warlords who happened to support the Empire”). The most notorious one is Ætius, but Stilicho, a Roman of Germanic origin, deserves credit as well. However, this importance of warlords also became a political liability: the case in point is the career of Ricimer, who acted as an apt commander and successfully defended Roman interests, but then provoked the fall of his former friend Majorian, who was the last energetic emperor in the West. In fact, the “fall” of the Western Empire is the recognition of a state of affairs — the struggle of the Empire against barbarians had turned into the struggle between war leaders who thought that supporting the Empire was the most profitable choice, and others who did not. On the contrary, the East proved relatively more stable in this regard, perhaps out of luck, but also because instead of being powers behind the throne, influential soldiers actually became emperors. A case in point is Zeno, an Isaurian (= member of a tribal group from the mountains of Anatolia), whose birth name was Tarasicodissa. Leadership was clearly more solid in the East.

• The pressure of barbarians happened to be much more intense in the West. One of the most important military events is probably the fall of Africa to the Vandals after their landing in 429, which deprived the Western Empire of one of its wealthiest provinces. Generally speaking, invasions/migrations and movement were constant. In the East, the 5th century was reasonably peaceful: Goths turned their eyes towards the West; a peace had been signed in the 4th century with the Sasanian Empire, which had to deal with the unrest of the (quite mysterious) Hephthalites in the North. Another factor which may, or may not have important, is that the landed élite in the West tended to have important latifundia, while property in the East was apparently less concentrated; and as a rule, it is always harder to get taxes from a few magnates than from a great number of small peasants. Even without taking this possible cause into account, it is clear that the Empire had less money to deal with more threats.

• Finally, an important factor to account for the 1000 extra-years of the Eastern Empire could be Constantinople itself. The city was shielded from Eastern attacks (Persians, Arabic invasions) by the Bosphorus; and it was protected from forays coming from from the West (nomads, Slavs) by a series of defensive walls, conceived to be almost unassailable. In many occasions, the survival of the Eastern Empire relied on these very walls — without them, for instance, it would have fallen in 626 during the joint siege by Avar and Sasanian forces. Ravenna, which was endowed with a naturally strong position, could have had become this (and did in fact play this sort of role at some points), but, for various reasons, did not manage to save the West.