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It's been me initiating our conversations via IM for about 3 days so I don't want to seem needy - although I am happy to come across persistent as I'm a persistent person about things I want in life!
Persistence is a great quality to have, but don't use it right now. You do seem needy currently, and in her eyes, weak. She has the power, you keep crawling back to her. Just stop talking to her. This can build interest, and at least doesn't continue the look of neediness.
Either she will contact you or not. If she does, then the freeze out has worked. SLOWLY move back in to talking to her. Reward her coming back by not bombarding her!
If she doesn't start IMing you again, then you didn't have a shot, even if you kept at her. She's just not into you.