Well, it seems I can answer that myself. After downgrading back to 10.0.4 and noticing the same behavior, and checking thoroughly the sound settings, I noticed that the option "keep the audio source active" was unset. I guess I had it set originally to "Always", but it did get into an undefined state after an upgrade to 11.0.1 and remained after the downgrade as well.
Setting it to "Always" solved the problem.