I researched this issue today. Many of us, myself included, have had times where we sent a PM to someone and it stayed in our outbox for hours and hours. This is actually by design:
https://www.phpbb.com/community/viewtop ... 6&t=841175
The basic gist of it is that when you PM another user on this board, until they log in and see their inbox (regardless of whether or not they actually open the private message) the message will stay in your "outbox." The message leaving your outbox is not a guarantee that the receiver read the message, but rather that the entered their inbox. Interestingly, you can delete or edit messages in your outbox, and they will change before the receiver reads them while they are there.
Thanks again to phpbb for their forums, which help us all here