I havent experienced this directly, but I seem to remember reading that if powerwalls are empty they shut down to preserve the battery (so they dont run all the way to "zero" but go into a conserve power low state), then they check every so often for power being generated so they can start filling back up again.
I cant find it, but seem to remember it was something like once an hour or something like that, the powerwall would wake up and check for power. I realize there are a lot of "I seem to remembers" in this post, and I cant find where I read it, sorry.