I think it's a question of applying a strict cost/benefit analysis to each new acquisition.
In the Western Empire the regions around the Mediterranean were reasonably wealthy. They were also relatively Romanized to the degree that most often a full legion wasn't even necessary to keep order. Thus with minimal military overhead, those acquisitions could be considered profitable.
The further we get outside the Mediterranean, the less wealthy the regions seem to be. The less Romanized the areas are as well, thus requiring more military overhead (three Legions in the comparitively small land mass of Britannia, for instance). The returns from conquest start to decline and probably become negative once we get to Britain.
The Romans though were not guided by accounting principles in conquest so much as cultural ideals - empire without end, bringing "civilization" to far flung barbarians, and bringing honor and glory to the commanders who conquered them. In that sense, conquest for its own ends probably made the Western Empire unstable to begin with. They did not have, and were not interested in, the basic rational analysis employed by every modern company.
The Byzantine Empire was, compared to the West, wealthier and in a better defensible position. It was simply more profitable, and thus able to survive longer.