How long does it take to find about a medical waiver to enlist?

My son Zach, Eagle Scout & VT Grad, is trying to enlist but requires a medical waiver because a physicians assistant prescribed him an anti-anxiety drug for 3 months in his Junior year at VT (3 1/2 years ago). He submitted his paperwork along with letters from our family doctor and a psychiatrist stating he does not need the meds back in February/March but has not heard back from MEPS. His recruiter also has zero information. How long should this process take? He is working as a waiter waiting for approval but is getting discouraged.