I’ve continued to see the problem with my Fossil Q Explorist smartwatch that appeared after installing the H update to Android Wear. Today I found a recommendation to turn off Mobile Battery Saver and so far since I have done that I have not seen the problem.
Update: Alas, turning off Mobile Battery Saver wasn’t the fix, the problem reoccurred. Next step is to turn off the always on display. I’ve also sent a message to Fossil to see if they can tell me how to downgrade.