To me, it sounds like the most likely cause is battery degradation. As batteries get older, they sometimes no longer discharge in a graceful way. In a “normal” battery discharge, the battery voltage declines gradually as the battery is being discharged. When a Li ion batteries get older, they sometimes experience sudden, large, unexpected voltage drops during discharge, especially if the discharge rate is high. The watch electronics need a certain minimum voltage to operate properly. When there is a sudden, unpredictable drop in the battery voltage below the minimum level, the watch cannot react fast enough to handle it gracefully, provide warnings, etc. It just dies or attempts to reboot as many people have described. The various solutions that people have offered such as turning off WiFi, background apps, etc. are all actions that reduce the load on the battery, i.e. the discharge rate. Under low/normal load conditions, the battery voltage may behavior ok and decline gradually, but under the higher load conditions, the sudden voltage drop may occur. When the watch is in exercise mode, it is continuously active, and also measuring heart rate, both of which add a lot to the rate of battery discharge, thereby setting up the conditions for the voltage crash and the watch shutdown. You can employ the “workaround” strategies of reducing load by turning off WiFi, etc., but this is likely only a stopgap as the battery performance will continue to decline and, eventually, even the reduced load will be too much. My suggestion is that you consider having the battery replaced. I think Apple will do it for $79, or you can take it to a variety of repair shops. I suppose there are kits to do-it-yourself, but I don’t recommend it, especially if you care about the water resistance.
I have a Watch 2 that is experiencing this issue. Turning off WiFi has helped, so I will use it this way for awhile, especially since it is an old watch that I only use for exercising. (I have a newer one for other times.). But I think the battery’s days are numbered...
I see that some people have sent their watches into Apple, and Apple has returned them saying the diagnostics check out ok. But unless their diagnostics test the watch under high discharge conditions, they may not detect the problem. The rate of battery discharge and voltage decline under low load conditions may look ok in their diagnostic test, so they may think that the battery still has adequate life left.