I think complete capitulation would just hasten him being removed, especially abandoning Italy, given its unpopularity as stated.
The only ways to keep Metternich are for either him to engineer a Compromise Constitution which is accepted by everyone, perhaps not embraced, but accepted, or for there to be a total victory on the part of the Austrian Military.
I think the former is more likely, but the latter isn't necessarily impossible. The Austrian Military managed to smash in the Italian's Faces so hard the King of Sardinia was forced to Abdicate and his successor had to run to Mommy France to stand even the slightest chance against Austria.
But yeah the Former is more likely. If Austria were to officially declare their support for granting the Nationalities that were counter-revolting against the Hungarian Revolutionaries their own states within the Empire, plus some constitutional concessions marketed as part of a comprehensive reform, I think that would give them enough support that they could pretty easily put down the Hungarians and restore Order.