I find the PM function on mobile is a bit buggy and Chris is aware of what I've reported so far. I've just noticed this same problem you are reporting now so this will add to the list.
BTW, check your sent PMs on your desktop if you get a chance. Some of the sent PMs might be there.
Ok, I just checked my Sent PMs on my desktop, and the ones sent while mobile are NOT there... . So it appears nothing is really tracked when you are using the PM function on mobile! I guess that means they don't count against your limit either?
one thing thats interseting, is that even after you delete a pm you can still reach it by going to its url.
not that it has anything to do with your question....