On the new firmware of these smartphones based on miui 11 and miui 12, this ultra power saving mode has appeared, it is briefly described here https://ru.c.mi.com/thread-1882127-1-0.html - this is the xiaomi forum. In this mode, and the Eset Parental Control program on the child's device does not block its inclusion in any way!, the smartphone system leaves only some system applications, and also allows the child to add their own: i.e. games, browsers, etc., and the Eset Parental Control application is completely unloaded from memory. When you return to the main mode, you need to enable Eset Parental Control manually again. At the same time, the Eset Parental Control application itself is configured correctly in normal mode, all functions are enabled: service, auto-upload, access over windows, etc., power restrictions are removed, and it works correctly and reliably. Do the developers of Eset Parental Control foresee a solution to this problem? Perhaps you should block the exit by pressing the button from the control panel to this ultra power saving mode? Otherwise, there is no point in using Eset Parental Control at all.
The technical support service did not respond clearly. They just send instructions on how to set it up correctly. But everything is set up correctly, just Eset Parental Control does not take into account the presence of ultra power saving mode in Xiaomi smartphones, as I also wrote to them. To which there was no reply at all.