You know, I was about to start an AH thread on this exact topic, about this very PoD
One advantage we have (at least) for the W. Roman Empire even in this late era is that the Hunnic Empire had already been shattered, so Attila is not a concern as it was a couple decades earlier. I'll go for the presumption that only the Huns were truly bent on the annilation of Rome. Just as Ecthelion said above, the Germanic invaders at least were comfortable with the idea of a vestigial empire, and content with occupying Gaul and Iberia (presuming the Britain is an entirely lost cause).
Historians seem to agree that Majorian was the last capable Roman leader. I really don't know much about Anthemius, and Ricimer seemed too concerned about his own skin than the preservation of the empire. Majorian assured the status quo in Gaul by defeating the Burgundians and Visigoths, so Italy itself might be safe for a while.
Now, if we have a longer reign for Majorian, instead of an ignominous assassination, and a successful recovery of North Africa, I'm positive that it could have given a lease of time for the Empire, more so if the Eastern Empire provides military and financial help.
After that, I suppose they would have to focus firstly on Iberia instead of Gaul, perhaps imitating the early Republican expansion after annexing former Carthaginian possessions in 3rd b.C. After that, if the Domain of Soissons manages to survive a while longer against the Frankish onslaught, the Romans could join forces to at least submit the Visigoths in southern Gaul into a client state, and even keep Clovis' hordes at bay in the Netherlands.
Of course, I'm butterflying away the internal usurpers and conspiracies that eventually killed of the last capable rulers. If instead of Ricimer we could have another Stilicho or Aetius that contributed to the cause of securing the borders of Italy and Africa at least, I guess the WRE can survive a while longer, perhaps later holding of an Ostrogothic or Lombard invasion.