There is little we can do to change that I am afraid, however there are a few things you can do yourself.
If you don't already try role playing your character, play by their traits and take actions that their character would even if you know that from a game play point of view it would be a bad idea.
Once you get to the top try and artificially create a bad scenario, get the crown in debt like Robert did or father many bastards and have your own Blackfyre Rebellion.
If you really want to spice things up once you get to the top console switch to another house and play with them.
These are a few of the things I do to keep my game fresh and long lasting