If Austria doesn't win the first election (usually because of a daughter or because Frederick dies way too early), its not going to get it back anytime soon. Unless Bohemia gets it instead I'll restart that game because any other Emperor is too weak to properly protect the Empire.
There is a very long list of modifiers for the voting process, and Saxony just seems to be ticking all the right boxes - and Austria might not even be trying to become Emperor.
Not entirely sure another modifier would have much effect, there are already modifiers for tag size.
That reminds me that I just saw them push the sanction almost instantly (within 2 years at most I think) in my latest run and they somehow still held on as emperor. I've never seen that before.
As for Bohemia, generally I'd say they're okay at protecting the Empire as well, but they're the only exception and they're certainly not as good at it, and with Austria going on an absolute rampage in the HRE once they lose the title (I'm still not sure if that should be happening over them trying to take it back), it rapidly becomes a mess even in the best of circumstances. If it goes to someone like Hesse on the other hand... yeah, the empire's only hope is for the player to become emperor (which is what I did as Prussia).
And that's the point for the most part - for the sake of the empire, the major powers in it like Austria should absolutely be encouraged to get it back once they lose it, or even if they're just in contention one way or another. As it stands, they become a bloodthirsty monster every time they lose it right now, and that dooms them forever. Even in the best of cases, Hesse in particular LOVES RM-ing and allying as many electors as humanly possible, and that's hard to fight against even for a non-bloodthirsty AI Austria. Even I as GP#1 Prussia had problems with Hesse and barely took the title from them (thank the endlessly warring and expanding electors for that), and Hesse is certainly not the only one who acts like that.