I've never heard of anyone actually saying they successfully regrew their teeth or parts of a tooth. I don't think the foods and drinks we consume help us most of the time, but I also do not believe the body evolved to be so oblivious to healing certain parts of itself which grew in the first place for a good and functional reason. So I'm inclined to believe that teeth can indeed heal, only I think we need to strike a fine balance enabling this because it's likely something that operates at a slower rate than the rate that we expose them to damaging compounds.
I hope you've found some success. I just realised this is a very old post!