Meanwhile the front panel controls go dead (and I think the
remote becomes ineffective as well), but the player keeps on playing.

This sounds like the old "Stuck Jiffies" bug, which is a known bug in 2.0 beta 11 and will be fixed in the next release (FITNR). You can also fix it right now by applying the Hijack kernel on top of 2.0 beta 11. Do you notice if the bug goes away after installing Hijack?