A proportion of claims are selected for verification, which is necessary to reduce abuse of the system. In general the turnaround for PAYE online requests is a couple of days; that's been my experience with using it anyway.
This happened to my wifes claim two years ago. She called her Revenue district and it appeared her Revenue had got "stuck" in the system and she got her paperwork and refund a few days later. I am not sure what exactly Revenue meant byt stuck in the system, but the phone call defo worked
Ive always found Revenue to be super efficient and good to deal with on the phone. You may be on hold a while waiting to get through, but once you do its usually dealt with quickly.