My thanks to everyone who posted above. I've had my Visio for about 8 years, use it every day, and never had the power problem until the past few months. I suspected it had something to do with the fact that I'd cut the cord on cable about a year ago. When we were on Comcast cable it never happened, but now I'm using Roku. My other set (a Panasonic) is also on a Roku and it's fine, no problems.
So, based on the advice in several posts, I:
* Unplugged everything, and pulled the Roku out of the HDMI port.
* Plugged the Visio back in, then did the factory rest (picked Menu on the remote, System 》Reset&Admin, then skipped all steps that involved connecting the tv to a network)
* Plugged the Roku power back in on the same extension cord (limited outlets available) and then plugged it into the HDMI port
* Used the Visio remote to select the Roku as Input
It's now been running for several hours with no shutdown! YEAH!