I do think immortality could get boring.
But there's something else, something more immediate. A line I remember from the Vampire Chronciles was one rather old vampire saying "The world changes, we do not. That is the irony." I'm old enough now that, when feeling particularly sour I said something about not liking the music now, the attitudes now, etc. And in the next sentence, I admitted that my father felt that way about current times when I was in my 20s. The world has changed and I don't fit in quite so well anymore. Some of that change is the physical aging of course. If my physical body were rejuvenated to 25 no doubt my libido would get a charge. In dealing with people, I think all the hard earned experience and knowledge I've gained could be put to good use (old saying: "we get too soon old and too late smart"), but would I really embrace the gestalt of today? I'm not sure. And I think the 25 year olds of today would know there was something different about me even if I looked like one of them.
Here's something else from a more philosophical point of view:
Even if you continue to live, are you still the same person? Sometimes, when I remember stuff from way back, it almost seems like I'm examining the memories of a different person. If you don't change, you're not really living, just existing, but in changing, the old you disappears a little bit at a time.