If you ignore them then the relationship deteriorates and you lose any bonuses associated with maintaining it. I'm not sure things could get to the point where they ended or not. Frankly I was so bored with the game I didn't care and just traded it rather than find out. I disliked being punished for not participating in the worst aspect of the game though, and I absolutely hated that these characters would call you fairly often, usually while I was on my way to do something that I actually had some minor interest in doing.

It was a terrible idea, and it made an already bland experience cross the line into really annoying territory.