@Jorath, can't say I've ever been in that kind of a situation, but it's the sort of thing one expects to find in the movies.

I've generally remained friends with my ex-girlfriends, though I can't say I've been in touch with any of 'em in quite a number of years.
If you like her, and you're not maried or currently in a relationship, you might consider hitting a lunch or taking in a concert together. Not necessarily to build anything, but just to show some a little sympathy and support. Single parents are usually under a lot of strain, and can use all the friendliness they can find. Just a thought.