The fact that you have had this issue with 2 different Apple Watches, would point to your power source.
- The power source could be the charging cable. The base testing should be done with the Apple provided charging puck.
- It could be the USB power source, which can be one from Apple, or a 3rd party, or even plugged into a personal computer USB port. It would be preferred that you use an 18 to 20 watt (or larger, such as your Mac's power brick) as the testing power source.
- The wall outlet you are using (a co-worker kept having his system reboot; installed a USP and found that every so often the UPS alarm would go off; turns out it was a bad wall outlet). The outlet could have a bad ground, or it could have an intermittent connection inside the wall.
- The power coming into your home (least likely, but we are fishing here, and a proper engineering solution means you think about all aspects).
The Idea is to change things to see what might be the issue, but using Apple manufactured items if at all possible during the testing.
NOTE: I have successfully used 3rd party charging puck for my old Series 4, and I've used many 3rd party power sources, my current being an Anker 67watt charger with 2 USB-C and 1 USB-A port which I use to charge both my Series 10 and my iPhone. The Anker is sufficient that when traveling, I can charge my Mac with it. But I AM NOT saying you need to ONLY use Apple cable and power sources. But during testing if you can use Apple items, it helps establish a base line.