Well, it's not like I only spend time with her because I like her. Her son is 4 and mine is 3, so we make plans so they can play together. Lately, we go out to lunch/dinner/etc. together a lot. We have a lot of stuff going on in our lives that's pretty similar, so we always have someone to talk to who understands. I don't really consider what I'm doing "persisting" at anything, because I don't expect us to be more than friends.
Now, I need to find a distraction to get this topic away from the Friend Zone and discussion of my personal life. Though I do love talking to strangers, I still don't like being the topic of the conversation. >_>
Edit: I guess you pretty much fail at avoiding being a topic when you do something like this. Son of a page.