Friendly Dilemma

One of the regular posters on a message board I sometimes visit (I will call her Cat) was talking about a girl she used to be friends with but has grown away from. This other girl still feels very close to Cat and tries to keep the connection strong, including trying to get together with her in person frequently. But Cat is busy and does not particularly want to hang out with her old friend, but doesn't want to hurt her feelings by saying so.

When I read this, I worried about whether I am being the other girl in any of my relationships, annoying someone who I think really does appreciate my friendship but is really just trying to figure out how to get me to leave them alone.

Later that day, one of my friends said something about how she sometimes feels unwanted by her friends. I've felt that way too, especially when it seems like nobody has put in any effort to contact me for a while. And I don't want any of my friends to feel like I don't still care about them or want them in my life. The best way I can think of to keep them from feeling this way is by reaching out to them, calling or texting or writing.

But if they don't want to still be my friend, I don't want to be the annoying former friend who won't leave them alone.

So how do you tell which friends really want your friendship and which would rather you just move on with your life without them but are too polite to say anything? Especially when the friendship is long distance.