Today is the second time that my Apple Watch showed the "I'm not connected to the iPhone" icon even though the iPhone was nearby and both had Bluetooth turned on.
The first time this happened, I didn't even notice. I got a Low Power notice from the watch, and concluded, incorrectly, that the watch probably had not been placed properly on the charger the night before and had failed to charge, and that the devices had disconnected because the watch was out of juice. However, the next day my watch was running low on power again, without me having changed any settings, and after verifying that it was fully charged in the morning. Therefore I conclude the watch was running out of power because it kept looking for the iPhone to connect to. (Usually one charge lasts me easily through the day; I use up about half its charge.)
I couldn't figure out how to connect them again, and ended up resetting the watch, losing my activity progress for the day. No big deal, it's not like I'm training for the Olympics or going for a Guinness Book of Records record, but still annoying.
So when I noticed it again today, and saw that my iPhone strangely claimed it was connected, but the watch said, "I know you are, but what am I?", I thought I better ask the interwebs.
Found several tech articles about this issue, and switching the Apple Watch into Airplane Mode and back again, as recommended on MacRumors, fixed it.
iMore has more options, parking this here in case I'll need it in the future.