Incapable is exactly the character trait that would Prevent you from abdicating. That's the drooling imbecile who rules for 100 years with his sonand heir as his regent... like Hoster Tully, Lord of Riverrun from Game of Thrones. Or outlives multiple generations of his heirs, like Walder Frey.
Abdication was, from what I remember from history class, generally a thinly-veiled way to legitimate usurping the throne, like king Edward II of England or Magnus IV of Sweden (both from Wikipedia). It was never really used as a voluntary diplomatic move until much later in history.
On the other hand, I know of at least one Byzantine Emperor, one Bulgarian King and one Ottoman Sultan who abdicated voluntarily (and in the latter two cases made a return when the son got into a bit of trouble). As I said some cultures... (Henry VI is of course a counter example).
And erm, Game of Thrones for all its historical inspiration is still fiction (leaving aside that nobody is contesting that old people can still rule, and Walder Frey isn't the type who would choose to abdicate).