I just upgraded to 3.8.2. Unfortunately the behaviour is unchanged.
It also seems to be getting more prevalent (by which I mean the number of users missing in autocomplete seems to be increasing, and more users are noticing the problem and getting frustrated).
Even worse, it's hard to open direct chats to affected users - creating a chat and typing in their username doesn't work (they're not in the popup, but even if you type their correct username anyway, you can't add them to the list). The only way I know of to open a direct chat is to click on their avatar in a channel and use the Send Message link, which does still work.
There are no errors in the log since restart (set to INFO level).
This has become a fairly big problem for us. I am surprised nobody else has reported it - I am wondering what could be different in our installation.