I'm happy at times here on earth despite many bad memories, and I'd be quite willing to take my chances with eternal life in some kind of "heaven" (whether naturally or supernaturally produced, and whether the bliss were perfect or not). The passage of time greatly reduces the pain of nearly all memories (all that I myself have experienced). Also drugs, meditation, therapeutic techniques, ordinary distractions, or just being in a good mood can take away their sting.
The woman I mentioned in my example was close to normal in her personality and intelligence, and her memory of most of her life was normal as well. If I'm not mistaken, her only abnormality was that whenever she went to sleep she would forget everything that happened the previous day. So I suppose that her sense of personal identity would be about as strong as ours.
Her situation was almost the opposite of the premise of the movie Groundhog Day (with Bill Murray and Andie MacDowell). [This paragraph reveals what happens at the beginning of the movie. It doesn't give away the ending, though.] The Murray character lived one day at a time, the same day over and over, remembering what was about to happen. He could modify the events of that single day. The next morning, though, the clock radio woke him up with the same Sonny and Cher song, and the same day started over again. The woman I referred to lived her day with a sense of complete novelty, without remembering anything that happened the previous day. Any changes that she made to the world were there the next day, but she had no memory of them.
BillyJoe said:
...it will go on and on and on. Can you not see the horror of that thought?
No, I really can't. Of course, I wouldn't want to repeat Groundhog Day for eternity

, but I don't believe that eternal life would have to be like that. It's the thought of annihilation, and not eternal life, that I find hard to accept. Ordinarily I try to avoid contemplating it at all. Our emotional reactions to these concepts seem to be very different, and it's not likely that anything we say to each other will change that.