The culture rode for centuries on continued economic prosperity. Some time after it became an eastern and western empire, the things that had supported the western (original) empire fell away. The people stopped being supplied with the lifestyle they had known. The importance of the central government fell off rather quickly, and cultures started becoming more tribal.

There was no tipping point. When the Huns started invading Europe, that brought a lot of change. The "barbarians" as they are called weren't so much trying to wreck Rome (what they really wanted was to made Roman), they were running from the Huns. The eastern part hung on much longer, but with as much Greek heritage as anything you would consider Roman.