I too could not find a record of mine from 1988, so after misplacing my old one (left it in a copier), I just went ahead and got a new one
No one mentioned it, but the fee for the FCC RR permit is 55$. The permit should arrive in about a business week if you use the online app and payment. If it has been a lot longer than that, I suggest you call the FCC at 800.225.5322 and select prompt #2 to talk to a FCC rep, then have them make sure your app and payment went through correctly.
In my case, the app (form 605) went through fine, but the payment did not for some reason. After figuring out what the problem was the second try went just fine.
Good luck