I was actually just searching the google box for this very same issue. I used to use a Wahoo Tickr and the same "Not connected" under Health Devices would happen to me. Only, with the Tickr it would actually unpair. I recently changed to a Polar H10 and am currently running a test for this concern.
1. I've enabled Power Saving Mode on the Apple Watch to disable the HRM during run workouts.
2. I've "paired" my H10 with the watch as a Health Device.
3. I've put on the chest strap, opened the Runkeeper Apple Watch app and began a run.
4. The Apple Watch is sitting on the charger and not on my wrist and I can confirm the HRM is off.
5. The Runkeeper Apple Watch app ran for 20 minutes with my HR displayed in real time.
6. During this time, the H10 became "not connected" yet remained connected and actively broadcasted my HR.
7. During the "not connected" periods, I began to breathe very heavily spiking my HR to confirm the H10 was still in fact collecting HR data.
It seems as though the concern we are experiencing is some type of WatchOS bug. I can also confirm that I have, on several occasions, put on the H10 and just started a workout trusting the apple watch would connect automatically. The results of those workouts would appear as though the chest strap worked as expected with consistent HR data.
Hope this helps!
Here is the results of my test above...
