Well, why bother to call it "the Holy Roman Empire" if it is really going to boil down to being just some kind of German Confederation?
If it really is a consensual and federal union, why shouldn't it include non-German nations like Bohemia or major parts of Poland in a non-subordinate role?
For that matter both Czechs and Poles would tend to strengthen the "Holy" aspect.
Which is quite problematic if by HRE we really mean "early edition Germany" because of course Germany is divided between Catholic and Protestant regions.
And the "Roman" part is a big red herring unless Rome, and hence at least a lot of Italy, is included. Trying to make it so and keep it so proved a major distraction from the mission--assuming the early HRE emperors (Hohenstaufens IIRC) should have chosen to accept it--of forming the nucleus of a German nation.
So all in all, I have a rather different perspective on what the HRE "should" have been--either a true pan-European Empire, and thus only partially German, or at any rate the greater-than-Germany central European Empire it generally was--including pretty much all of Germany, but also the Lowlands, parts of Italy, and Bohemia.
The problem, as the posts here with their narrow focus on averting or defeating Napoleon already acknowledge, is that key parts of the minimum whole were held by powers peripheral to it who had strong interests well outside the boundaries of the traditional Empire. And this was always a problem--basically because any European dynasty strong enough to hold the core of the Empire probably rose to power outside of it and brought these distant peripheral possessions in--but none of them could strengthen the unity of the Empire to the point that these outer realms got irrevocably attached to the whole.
in the end, most of what people here are talking about as the "Empire" did indeed become one--the German Empire, taking its organizational core as the concept of a German nation, to the detriment of various non-German minorities within it.
So--with a POD well before 1789 and all that, I might accept that a stronger HRE consolidates itself, and de facto is recognized as mostly German and the natural home of all German states; given the realistic trends of the Modern period it seems likely that minorities would indeed get eclipsed--along that path, we have basically the First Reich sequeing into something like the Second Reich, probably with somewhat more territory. If the nationalist principle is strong enough perhaps Bohemia gets ejected; perhaps Austria, with her long-standing possessions and preoccupations south and east, gets ejected too.
Or somewhat more interestingly if less likely, we see the Empire evolve into something more multicultural. It seems that much of the sentiment expressed here for the HRE revolves around the notion that the Empire would have been confederal and so the numerous statelets of Germany prior to the 19th century processes of forced unification might have persisted, perhaps in a royalist/aristocratic analog of the USA's federation of republics.
Well, that's a pretty romantic idea. How it would evolve in practice without simply as OTL being an open invitation to disintegration and providing a battlefield for peripheral powers inside and outside Germany to fight over the pieces--that will take some ingenuity to explain!
The alternative that was seen at the time to balkanized chaos was that some single strong power should take charge of the whole and ramrod it all into what the name of "Empire" suggests it aspired to be, a single centralized unified state. And of course the various established intermediate powers spent most of their time making quite sure nothing like that ever happened, going along with a strong centralizer only insofar as it might help them balance the score with some local rival--then it was time to switch sides and fight the centralizing power. Or better yet, don't elect an Emperor in the first place who has any prospect or program of centralizing!
The idea of the Empire evolving into some kind of liberal Common Central Europe, with or without some established religion (but if "with," it had better be an especially tolerant one, given the fundamental split between Protestant and Catholic, plus of course one would prefer to avoid the brutal suppression of yet other religious sects that OTL were crushed in the region) is appealing enough but I don't see how it could reasonably happen.
But anyway here we are talking, per OP, about taking the Empire as it was in say 1800 and keeping that going. I humbly submit, by that point it was little more than a political trophy, one that had been captured by the Hapsburgs but emptied of all deep significance. Logically the Austrians should either have dispensed with the title or extended it over their entire realm, on the theory that the reborn Roman Empire does aspire to rule the entire world eventually anyway. They couldn't do that of course because the various German states within or partially within the Empire but not under Austrian control would object to the Viennese Emperor packing the Electorate with distant Electorates in his pocket. Which goes to show--the Empire may have served some sort of function but was hardly a unified nation, nor even a confederation based on any deep appreciation of mutual interest.
Now--suppose that both the Hapsburgs and the Hohenzollerns had suffered some severe reverses around the turn of the 18th t0 19th century, and it proved possible for several medium-sized German realms within the Empire to work out a sustained joint common policy for the collective defense of Germany-or perhaps even from the beginning, some of these medium powers could have been non-German--the Danes, the Dutch, the Bohemians, perhaps even some Italians...and they found the old framework of the Empire useful, electing one of their number as Emperor, perhaps picking up the pieces of broken Austria and/or Prussia. If the policy of cooperation proved workable and mutually beneficial to a fair number of key statelets within the old Empire bounds, I can see them working together to maintain and modernize the federal structure and under that rubric, keeping the HRE on the map as a real political unit.
But this is a stretch too--more likely one or another of these medium powers would seek to go it alone as Prussia did OTL.
I suspect that even if Napoleon and indeed the whole existential challenge posed by the French Revolution OTL were butterflied away, the HRE was most likely doomed to continue fading from real-world political relevancy, even if perhaps it might still exist on paper to this day.