A lot depends on the list of claimants (when you get the 'you have a new monarch' screen) and how powerful they are and how they feel about your new character. Over a very long reign, you can build up a nice, fat 'long reign' modifier with all your vassals and a new monarch gets a 'short reign' modifier that counts down every year. And if you do have harsh laws that makes matters worse. I think that dukes who have claims to the de jure kingdom that they are part of will make that claim pretty often.
Well my brothers stay loyal, the problem is those pesky dukes, that has no claim what so ever wants to constanly lower authority of the crown, will they never learn? The size of my land is big i get a lot of prestige. after each civil war that happens every single time i change crown i have over 3000 prestige. I Always give my heir duke title early on.