I think you would need major economic reform and an end to corruption.
Abolishing corruption in a pre-modern state is ASB: the Roman state would have been entirely unable to function without what we class as "corruption".
As to the OP: the WRE needs a little more luck, to be able to deal with its enemies piecemeal. By far the best late-ish PoD is to have Constantius III survive for another 5-10 years in the 420s: a capable soldier Emperor on the throne who is married into the Theodosian dynasty and focused on expelling the remaining barbarians. With a bit of luck, a surviving Constantius can mop up the remnants of the Vandal-Alans in Iberia, and prevent the Visigoths in Aquitaine from getting too uppity. The WRE thus has cash flowing in from its Iberian and African provinces in the 430s and 440s if and when the Huns hit.
Butterflies mean the Huns are unlikely to collapse as quickly as they did IOTL (if they even rise to superpower status at all) which is a blessing in disguise for the WRE, sparing it from having to deal with so many barbarian groups fleeing Hunpocalypse at the same time. An optimum scenario here would have the Huns firstly failing to gain as much power as they did IOTL, and then unravelling at a more sedate pace thereafter.
So, that gets the WRE into the sixth century, assuming a modicum of good luck. Good luck won't go on for ever, of course, and there's nothing to prevent the Western Roman state going under thereafter: there are still presumably going to be large and organised Germanic groups in this scenario who aren't yet on Roman soil, notably the Franks, Alamanni and Langobards. So, there will be challenges in future, but nothing that necessarily spells the doom of the WRE.
