You are annoying her. She was an aquaintance, not a friend. The money clouded things. She felt she had to be nice because she accepted money from you. (which she never should have done.)

Let go. You are only tormenting yourself.

Find other ways to be with people. Find male friends. Your attachment to her is unhealthy. Since she took the money, she feels she hasn't the right to just blow you off in a really obvious way, though she comes close to that. You are demeaning yourself, looking for crumbs of attention. Take a hint. She's given you enough of them.

A woman knows when a man is attracted to her. When the woman doesn't have a similar interest in the man, she will not want the man pursuing "friendship" with her, especially not a friendship that involves "hanging out." That is just a round-about way of trying to date.

You are lonely on two fronts. You wish you had friends. Also you wish you had a girlfriend. Nothing abnormal about those desires. What is abnormal is clinging to this lady who is not available in either of those capacities. You cannot buy your way out of loneliness by "helping" people with your money.

It can be hard to learn how to socialize successfully. It doesn't come natural to me either. But stop pursuing interests that are inappropriate and see what is left. There are healthier things you could be doing.

You've been going back and forth on this connection to this woman for a long time. You are truly stuck. Periodically you get frustrated enough to say it's over, like you just have. But you keep going back into wanting a relationship with this woman. Then you try and analyze to death how to cook up a strategy to reconnect with her. Please stop. This is wasteful of your time and attention.

Possibly, some therapy might help you. Spend your money on that. Help you.