Forgot to email a professor back about a research opportunity. What to expect?
I have a friend who did something similar. She didn't realize she had a job offer on her voice mail for several months. In this case, the job opening still existed and she still qualified, so they hired her anyways. I don't think there's any reason why this has to be any different.

On the other hand, she could quite possibly have moved on to other things or hosted someone else in your absence, in which case it might just be unfeasible for her to pick you up after all this time.

And there are many people who would refuse you just on the principal that you made a mistake. I've certainly met plenty of them.

At the end of the day, you've probably done all you can to rectify the situation. If she denies you, just move on with life. If she doesn't, buy her some cookies and be happy. :)