As a continuing saga ... I reported first on this a few days ago ... I have a v4 Apple Watch. I installed Watch OS 6.1within hours after it was released. The battery draining did not start until the day before my first post on this subject. Other than sign up for Apple Studies, I changed nothing in my v4 Watch between the time I installed 6.1 and the time the battery started draining rapidly.
I've done a variety of things, but, yesterday, with 50% of the battery gone by Noon, I had to put the watch back on the charger for a couple of hours so that in client meetings it did not die on me.
Right now, I've had it off the charger and running for about 2 1/2 hours and it's used 17% of the battery, without any music, no texts, and only occasionally notices.
The thing is, I support Apple and love its products. And, I am what some would say an 'informal tech opinion leader' in my area, and have influenced a great many people, just because of my word of mouth endorsement of its products, to buy Apple Watches, iPads, iPhones and even Macs. I was about to recommend the Apple Watch to a couple of friends who have health problems that they might be able to monitor more effectively with an Apple Watch ... but, with this malfunction (which is what it is ... calling it a "software" problem, just disguises the fact that whatever is causing this so widely is causing the watches to malfunction), I can't very well endorse the watch to anyone.
I hope Apple gets this fixed soon; I've wasted far too much time on trying to self-diagnose a defect in its Watch.