Why won't she give my hat back?

It's possible that she likes you. Is she giving you other signs of interest as well? If she is, then she might be keeping it because it is a) something of yours to have and b) because she wants you to have to come and get it, which means she gets to be around you a little more. If she's not giving you any other signs of interest, she just likes your hat and is goofing around with you as a friend.

This is fifty fifty

she mite have taken your hat because she likes you
and wants a reason to talk and see u

she mite just be hatin on your hat and wanted it and you gave it to her

Unless she says, "If you want your hat back, then you'll have to come over on Saturday to get it ! " I think she just wants your hat .

Maybe, but I doubt it - I think she just wants your hat - I've had girls steal everything from sunglasses, to hats, to even pants !

If she liked you, she have been doing it to encourage you to talk to her and see her again . Since you've asked her 4 times, I doubt this is the case - have you made plans and done them with her since she first took your hat ?