UPDATE
Since I received my replacement batteries, shortly after my initial post, I have experienced no further problems. I did have a couple of days when I thought I was experiencing battery failure, but it turned out to be 3 bad atomizers (topic for another thread, I suppose).
Recently I also purchased a defective USB passthrough in the meantime (and one additional defective atomizer). The passthrough was stuck in the "on" mode, and just kept burning no regardless of me taking a puff or not. Darn thing nearly burned my lip, too.
The problem with the passthrough was identical to the problem I had with the batteries. So, I conclude that the auto switch is a faulty design that's prone to failure. Manual batteries/passthrough seem more reliable, from what I've read on this forum.
Anyway, everything is working now, so I am happy.