Instead of it being a current duchy, would it be possible to make it so anyone in the realm can protest dukes? After all, if the issue is with one duke with only a few knights who support him in his duchy, making it so only the duchy can protest really does nothing.
If a duchy supports their duke, they should not be removable. Just like if a realm supports their ruler/government-officials, they should not be removable.
I also agree that ROyals and DUkes should be strong, but why in a Republic, does the royal thing even apply? It's a republic, not a monarchy.
Because its not a modern republic, but a medieval republic.