They might not have been able to stand up to the full might of Austria in the field once they mobilise against them, but what if Vienna finds that the Austrian generals inexplicably won't attack, citing vague "supply issues", allowing the Italians to seize strategic areas? Or perhaps, after a donation to a general's retirement fund by the Prussians, he decides that fighting Italians isn't really for him, and leads his men to go and fight the Danes in S-H in a 'war of national liberation'? In other words, the success of rebel factions is in part dependent on early wins (which they had in OTL) creating panic or pessimism in the Hofburg, and an environment ripe for Prussia to tempt any Austrians who sense a shift in the winds and want to be on the right side when its all over, into doing their bidding. Thus sending Austria into a negative-feedback downwards spiral
But why should it have that effect?
The Austrian half of the Monarchy was largely secure. It was of course annoying to have Vienna in rebel hands, but the Empire could be (and was) run just as easily from Innsbruck or Olmutz. Opposition elsewhere never amounted to much. In Cracow and Prague what little there was had been easily squashed, so the Austrians had a secure base from which to retake Vienna and the Italian lands, then get started on the Hungarians.
And Hungary's resources were meagre. She had just one arms factory, which had to be evacuated twice from Budapest to Nagyvarad to escape the Austrian army, a task which couldn't have helped production. And with Croatia firmly in Austrian hands, she was cut off from the sea, so could import only through Turkey, whose communications were poor and which was itself vulnerable to Russian threats. Add to that the fact that Rumanians and Serbs were up in arms in their rear, and I'd say the Hungarians did well to last even as long as they did. I certainly can't see the final outcome as being in any serious doubt, though I agree it would probably have taken longer without the Russians.
So Austria isn't going to collapse of itself. If Prussia wants to supplant it, that can only be done as it was done OTL, by defeating it in war - which in 1848/9 would probably have meant fighting Russia as well. And a King of Prussia who has (quite unnecessarily) allowed himself to be chased out of Berlin by a mob is hardly the man for that task.
One can of course envisage a tougher king, who gives the army its head and allows it to crush the rioters in Berlin from day one. But such a king, of course, will have no sympathy for revolution, so that we probably don't get a Frankfurt Parliament at all.