So... no luck on the Tribble theory. All of my empty mails are back now, showing no items on any character. The problems appear to have started after Season 3 was released and is incredibly annoying. I guess I have just been lucky not to glitch up until this point? I've only got about ~40 of these messages, but I've found forum threads where some people have 300 of them!
To: Starfleet Personnel Dept. Heads, local SB/STRSHP
Re: Starfleet Postal Service Targeted Acquisition-Retention Deployment
In accordance with the groundbreaking study published by the Betazoid Utilization Laboratories' Social Heuristics Team, the Federation Council has approved the expansion of the Starfleet Postal Service by 20%. These new positions are to be filled on a priority basis based on the B.U.L.S.H.T. recommendations in Section 25:31 sub A. These criteria, highlighted by the Learned Ostracism Social Exclusion Rating index, show that certain species are prone to systemic under-utilization. The species that placed highest on the L.O.S.E.R. indexes, the Pakleds, require special consideration to reverse this trend. The Starfleet Postal Service has been selected as the host organization to validate the B.U.L.S.H.T. L.O.S.E.R. hypothesis due to the relative benign nature of SPS's work. Positions are to be filled as soon as possible. All documentation regarding these L.O.S.E.R.s must reference this program (ex., Dirk Khrapstayn, Postal T.A.R.D.)