Judging by the chatter on other forums, there seems to be at least two problem periods. The first is early March, just after the reminders arrived. The second was as the beginning of April approached. It seems that most that bought between those periods got their licences in a few days, I certainly did.
I doubt that ringing, or visiting, the post office will do anyone having problems much good. It's the EA that most of the issues stem from, provided you manage to navigate the Post Office website successfully. The EA blamed the early March delays on printer issues.
Give the EA a ring and have all the appropriate details handy. Chances are that they'll just send you a duplicate licence. Next year, avoid buying (on line or over a PO counter) just after the renewals go out and just before April the 1st.