Depends.
OTL, it was just as riddled by usurpations as the rest. Its internal instability was, ultimately, its downfall.
If the PoD for its survival is some Reform which stabilises and strengthens it, then i don't see why a Roman successor state with such a manpower Base can't deal with a few Frankish and Alemannic plunderers. They might have a hard time when Vandals et al. cross the frozen Rhine in 406, but at least they'd have to try to fight back instead of giving up thei very own territory.