I have been in one of those relationships and I am friends with many transsexuals.
As for my friends, I do know individuals who remain with their partners during transition and even after. Normally, these relationships work when either the transsexual partner was very upfront about their gender identity from the beginning or the other individual knew that the were gender confused from the get-go. One of my friends has been with her partner for 11 years. About 8 years ago, she began to transition from male to female and it was her partner who encouraged her to transition. They are very happy together and have the cutest relationship. Her partner identifies as bisexual.
Ones where transition began later in the relationship tend not to go as well, but I do know some who are still together. I know some girls (I know mostly male to female transsexuals) who are now friends with their wives (because the wife was encouraging of her partner but not bi) and some who’s ex-wives hate them (normally the ones who came out after years of marriage.)
As for my own experience, I was introduced to an individual who identified as transsexual in 2001. Early on, she seemed to be more genderqueer (at least in relation to me), going by both “he” and “she.” When we first started dating, I would mostly refer to her as he (We lived with her parents and she wasn’t out yet to most people). If you were going to catagorize our relationship, then most people would say heterosexual, except that my partner was an extremely feminine male (people often ‘mistook’ him for a girl and we were constantly called ladies). We had a very strong relationship for two years but eventually broke up for a variety of reasons, none to do with her being a transsexual. About a year ago she started taking hormones and began the process to change her name. Now she has cute little breasts and a more feminine facial structure. We remained good friends and still sleep together on occasion. In fact, I am posting this from her apartment. 
I regard myself as bisexual. I seem to be emotionally attracted to women but physically attractive to men. To be completely honest, I prefer her male body over her female one, but I still consider her incredibly sexy. (I think she made a sexy guy and that she’s also a sexy girl.) Personality is the key for me and even if she was an ugly girl, I still would date her because to me, mind matters more than body.
As of right now, she regards herself as a non-op transsexual. If she finds a way to get the surgery done and has it, I would still be interested in a relationship with her, provided that all the other details were worked out. A lot of transsexuals do change while on hormones though. Lately she seems more interested in guys and I bet she will end up with one eventually. It wasn’t that her sexuality changed, but rather, she’s only interested in dating straight men, and it’s only in the past year that she’s been able to completely, totally pass. (Now random guys hit on her all the time and have no clue whatsoever).
I hope that helped. Feel free to ask any questions. 