I think it would depend on the relationship. If it were a friend or family member that I wasn't particularly close to, I could certainly re-establish the relationship. My thinking would be that if it happened again, well I tried, then I would forget it.
With those really close to me, the hurt would be much much deeper. I would certainly try, but I believe once trust has gone in any relationship, it will never ever be the same. So, a new relationship maybe.
With regards to my daughter- in- law, if it meant being allowed to see my granddaughter, I would do everything in my power to create the illusion of a relationship. That's all it would be though. The deep hurt of being deprived of my beautiful grandaughter in my life so far, and the pain this has caused my son too, will be with me forever. I can't forget that when I was alone and dangerously ill, she never so much as sent a card, text, or even a message via my son. Some things are too big to overcome.