Other people 
who have the Fossil Q Explorist are having issues with the Wear OS H update.
A contribution to this thread suggested enabling developer mode and then turn off mobile battery saver, which I have done. Let's see if that fixes the problem.
Well, so much for that idea... my watch is acting up again and I am not even wearing long sleeves. I did start a timer. I've now turned off the always on display.
I am trying to figure out what is mobile battery saver. So far I have the impression it was once called cellular battery saver , with implication it is a "feature" for watches with builtin LTE. However, if that is true, why was it enabled on my Fossil Q Explorist that does not have a cellular radio?
I personally suspect the problem I am seeing is more related to the "off body efficiency" referred to in this article .
Well, I don't know what is the actual problem, **but it appears that disabling the always on display prevents it from happening**. Perhaps the deep sleep feature doesn't kick in if you turn always on off.
Note in the change log of my Fossil Q Explorist that the problem has not returned since I turned off always on display. I have also discovered that with always on display off power consumption is dramatically less. I am getting through a day going through 25-30% of the battery whereas with always display on I can end the day with 20% battery left.