I live in an area where power and internet are not reliable. After a power outage my internet doesn’t return for a while. I an wondering after an outage, when power comes back without internet, will the wyze plug remember the correct time and retain its schedule?
Welcome to the community, @distortionist. The settings for your devices are actually stored in the cloud, so when power comes back on, they should return to what you set them to. 
Well a corollary question would be whether and how long the plugs will continue to try to phone home to the cloud as his or her Internet gets itself straightened out.
I assume they will keep trying indefinitely. But I think the poster is concerned as to just how long after Internet returns will the plugs be usable…
That is dependant on the ISP and the modem/router. I know this because my situation is very similar to @distortionist. After I had my ISP upgrade my wireless antenna, AND I upgraded to an Amplifi HD mesh, almost all of my problems went away.
Yes of course but I’m asking about the plugs’ behavior during that time.
With my old R7000, I had multitudes of issues with ALL my devices. If my plugs get an IP address quickly from my new mesh router after a power outage, and the internet is restored later, then they recover just fine.