This is a bit of a long post and my setup is a tiny bit different, but I have noticed something similar in one of the two cases I mentioned: LZW31-SN with relay disabled spontaneously turns off with low loads.
In the case most similar to yours, I have two LED bulbs in a neutral-wire installation, but the LZW31-SN freaks out when the bulbs’ power draw gets below some magical threshold and “turns off” but also becomes completely unresponsive to local or Z-Wave commands to turn back on. It does not seem to happen when the bulbs are at full power. My added complication that these are smart bulbs and so the actual power of the load can vary depending on their configuration, but with the neutral wire, I assume this shouldn’t matter.
Are you sure that pulling the air gap at the bottom of the dimmer doesn’t work? That works for me and should be more or less the same from the switch’s perspective.
I still don’t know what’s going on, but if a load that draws more current works around your problem, I suspect it’s similar to mine.
There is also this thread: LZW31-SN turns off randomly as well as this related questionnaire: Dimmer Switches | Random Shut-off Issue | Data Collection Thread. However, it’s not clear to me whether those people mean literally just turning off or the switch basically crashing and not only turning off but also becoming completely unresponsive unless power to the switch is pulled and restored.