Should you accept the approaches of a girl that has rejected you in the past?

I would not advise it. She cannot make up her mind, and just when you get sucked into wanting her, she is likely to change her mind and dump you.  Look for someone who is more stable and consistent if you don't want to get hurt.

It depends on why she rejected you in the past. If she was in a relationship, she was going through a tough time, she was focusing on her studies/work, or some other genuine reason that meant she couldn't be in a relationship with you but the situation has now changed, I don't think it's a bad thing to give her a chance.