I had a temporary crown done, it kept coming off. Haven't had anything on my tooth over a month, is it going to be damaged??

It is not a good idea to be without a temporary crown for this long.  Temporary crown protects the prep, gum, and tooth movement.  It should not take a month to get a permanent crown.  It seems that there might be other issues in play since your dentist is delaying putting your permanent crown.  I would go to the office and talk to the dentist if you're having a hard time calling.

If the crown is already paid for in full, what is keeping you from having the crown cemented on?  Ideally you need the permanent crown placed right away. The temp crown keeps the teeth from shifting and provides some protection to the tooth.  Sometimes temp crowns don't behave like we want and pop off.  I will sometimes recommend putting a tiny bit of denture adhesive inside the crown and press back in wiping away any excess.