It seems you can only go half way backwards. If I read it right here is how it works.

The way up
Monarchy-Parlimental Monarchy-Middle Class Revolt
Parlimental Monarchy-Republic-Lower class revolt

The way back
Republic-Parlimental Monarchy-Middle Class revolt
Parlimental Monarchy-Monarchy-Upper class revolt


To the best of my knowledge, there is no way to skip a rung of the ladder. The lower class won't revolt until after the middle, the upper won't revolt until after they've stepped back from a republic.

The only way you may be able to go from one to another quickly is if there was a war of sucession, but once you are a repubic to best of my knowledge there is no war of sucession.

From most of what we read it seems the people are far more happy in a republic, so it seems less likely it will revolt. Though as you can tax different classes, I assume if you are a republic and want to go back the quickestway is to tax the heck out of the nobility.