What sort of reforms would have been necessary to not only strengthen the HRE in its decline, but to possibly keep it going for as long as possible?
It really depends from what you search, and on which decline we're talking about. It lasted up to XIXth century after all (while the last century was really down), so it might be more strong than usually tought, isn't.
It lasted enough, at least, to know several crisis (and survive it) : Sacerdotal Wars, Welfs, Great Interregum, Reformation, etc. Depending which period you have in mind, very different things could be discussed (and keep in mind that emperors and imperial administration did launched, sometimes successfully, reforms of their own).
On a more general note, I think that reinforcement of the HRE (as not only Germany, but the whole imperial institution) would have to pass trough its own unique way.
As in, keeping a relativly open structure, not really centralizing as its neighbours, but unifying around the imperial kingship, as sort of a federation.
Given the historical situation of the empire, the challenges he had to face, and how it was definied, I think a centralisation as it happened in Britain, France or inside HRE states wouldn't work.
How would a federal empire look like?