Not sure if this is a specific case with just me but if I go to "sent messages" in my personal messages, I have only one from back in 2014. Is this another big ol' bug in the web site or...? (shrugs)
I believe you have to purposefully save a copy to your outbox by checking a box in the prompt. You likely just didn't do that. If you did, yes, it's a bug/issue of some sort.