Not your fault. Some people are compulsive talkers and it's one of life's major irritations! And, I don't think there is any hope or cure. It's majorly rude and I have decided I don't need anymore of that in my life.
I (gradually, without fanfare or rancor) stopped talking to a friend over this. She and I lived 1000 miles apart at the time, and when I'd call to catch up, it was a two hour monologue, and when she'd ask me something about my life, I could not even get a sentence out before she'd interrupt and be off again. My adored godmother always also had these tendencies, but when she lost her husband, it got a lot worse, to the point I don't see her as often as I used to because I can't handle the verbal diarrhea. A third person I know like this is my cousin's uncle, (whom I grew up knowing and also refer to as my uncle), but he's kind of a jerk in other aspects, so I don't see very much of him at all. Which is kind of sad, because he is all alone now and could use companionship and invitations to holiday gatherings.
As far as spending time with compulsive talkers around the holidays, if you have to be in the same place, maybe go into another room or find someone else to talk with if it becomes intolerable.