What to try:
1) Could you try to install AdvancedAutoAway (which is from same author as KeepStatus) and reproduce problem with it too?
I have tried it, and I couldn't reproduce the problem there. It's bug-free there. Cool!
3) Will enabling setting "Switch to offline before try new connection attempt" (I'm guessing name) of KeepStatus make any change to the behavior?
It changed the behavior, but it made it even more weird. After changing this option, it sets my other not-disconnected account to "offline" (so I had two offline accounts at this moment), and a few seconds later it's connecting with the status "away", ending up with the same result like before in my original post.
4) Could you also enable showing popups of KeepStatus behavior? (there should be some option for that) Maybe it would help understand what's going on with the first protocol that hasn't lost connection.
I have tried to do it, but somehow I don't see any popups, although the popup test in the settings is working. Sadly I haven't much time right now why it's happening even though I followed the steps of AnrDaemon. Luckily Friday isn't far away.
That's an interesting question.
Does KeepStatus watch protocol status changes between reconnects?
For me it looks like a no, but then it's weird why it doesn't happen with the "AdvancedAutoAway" plugin