How many times?

I think it would be safe to say two times (just to make sure). Anything other than that might get annoying. Does she already have a date for the prom? If not, ask her. If she says no, then move on :)

I wouldn't say there is a specific rule. If all her excuses sound fake or made up then she's avoiding you. I would stop asking at 3, just so you don't appear clingy. If you've asked her a few times and she keeps canceling she'll tell you when she's free if she really wants to hang out.

There's not really a rule as to when asking is too much. If her excuses sound like BS then yeah I'd stop asking right away. Girls give signs, you just need to look for them. If she turns you down for hanging out when you know she's not busy then that's a pretty good sign she's not interested, sorry :(

I would say 3 times would be the most you want to ask her to hang out. There's always the chance that she's just an honestly busy person, but you don't want to be annoying if she is trying to avoid hanging out. If she says no on the 3rd time, put the ball in her court. Let her know that you really would like to hang out, but she should get in touch with you when she has time. That way, if she wants to- she can. If not, you can talk to someone else and not worry about her!

After several incredibly frustrating situations that are very similar to this one, I've adopted my patented Three Strike Rule (tm). It basically goes a little something like this:

Any point of contact and/or initiation by you is a 'pitch'. Anything swung on and missed (for any reason) is a strike.

So, say for example, you leave her a voice mail asking to return your call and hear nothing back within 2 days - that's definitely a strike.

Any broken date for anything less than an emergency (think of excuses you could get out of class with. That's a decent paradigm), definitely a strike.

After the third strike, give her a seat on the bench and wait a couple of innings. (i love baseball)

It's your call on 'fouls'. Miscommunication, not calling you for an extended period of time because of travel, broken phone, etc. On several occasions, I've had girls 'foul out'.

Basically the ideas is this: it's definitely your job to initiate things, but it's her job to respond (either with acceptance or rejection). Lack of a response should be response enough.

Spend your time wisely on someone who feels the same way you do, and who won't waste it.