So I sent myself some mail. It got to me within like 15 seconds.

Later I noticed my bags were getting full so I made a "Bank Alt" which I leveled enough to get to a mail thing (5 or 6). Then I mailed him some of my items that unlock costume pieces. That was hours and hours ago. :(

I've reported a bug where you can loose items in the mail. It can get stuck on the "Sending items, please wait..." screen for a long time, possibly indefinitely. If you close the window or move away to get out of it, the item(s) sent are lost. This *really* should be handled as an atomic transaction, where it doesn't permanently remove it from your inventory until it's been confirmed placed in the mail system.