To me a prime example of change would by Nynaeve from WOT. As it is for a lot of people. When I first started reading WOT I couldn't stand her, but as time progresses (and I progress through adulthood - from early 20s to early 30s) I found an understanding for her character. I understand what's wrong with her, and I now see that beside the bad things she does, she's got her heart in the right place.

Rand I do not like as a character anymore, like I used to do in the beginning. But separate from this, I do still find it interesting to read about him. Maybe it's a difference between "liking the character" and "liking to read about the character".

From ASOIF, I love to read about Tyrion, but I can't say I like him as a character. Jaime was interesting, not anymore. (I say 'Sap'.)

Or what about LOTR? For some reason I can't read about Gandalf anymore, now that I have seen him in the movies being an all powerful wizard who does absolutely no magic, except waving a shining staff against a Nazgul (granted, thereby fending him off) and riding really fast.

Oh wait, that wasn't magic, that was Shadowfax.

Also, when a book becomes boring itself, it is hard to keep finding interest for the characters.