The why is unknown. The Apple Forum reported same issue on MacBook Pro M1. Next time it happens to one or both, test this =

* Mac Mini M2 Pro is on
* Disconnect the two USB-C cables from the Mac Mini M2 Pro
* Turn both U2722DE off
* Reconnect the two USB-C cables to the Mac Mini M2 Pro
* Turn both U2722DE on

Thanks a lot for your kind response! Will definitely do the suggested test the next time my monitors "misbehave" and report the result here.

A few moments ago, after waking up my monitors (they are set to go off after 5 minutes, not the Mac Mini, so no sleep for the Mac, only the monitors) only one went live; the other one remained unrecognized. I took the opportunity to run the test you had suggested and did the following, with Mac Mini M2 on:

* Disconnect the two USB-C cables from the Mac Mini M2 Pro
* Turn both U2722DE off
* Reconnect the two USB-C cables to the Mac Mini M2 Pro
* Turn both U2722DE on

Unfortunately, the situation was the same as before the test - one monitor recognized, the other not (the same ones).

I then did the test a little differently. With the Mac Mini M2 on:

* Turn both U2722DE off
* Disconnect the two USB-C cables from the Mac Mini M2 Pro
* Reconnect the USB-C cable for just the U2722DE that was "dead" and turn on only that monitor  - I got the message that I have no signal on USB-C and the monitor stayed dead.
* Reconnect the USB-C cable for the other U2722DE and turn on that monitor - it duly went on and the Mac continued to recognize only that one.

So I went back to my proven remedy, a little simplified this time - switched both monitors off, pulled out their respective power cables, waited a little, reconnected the power cables and switched both monitors on. They now both worked again and both were recognized by the MacOS as expected.

I have done some more testing. Now I connected one of the monitors with HDMI and the other with USB-C.  Soon enough, one dies, after a period that ranges from an hour to two days. The new thing now is that the USB C one also sometimes starts flickering after a while. Then I exchanged the connections a few times so that each of the monitors was tried on both USB c and HDMI. I also tried different USB C cables. The monitor dying (or flickering) was always the one connected to USB C.

I might have discovered the root cause. I was using the DDPM (Dell Display and Peripheral Manager - latest version available at the Dell site) that was running in the background. I have stopped that app and also removed it from the Open at Login list. Almost two weeks of heavy use later and with both USB+HDMI and USB+USB connections, after many wake-ups from sleep and also a few MacOS restarts, not a single incident! Both monitors work and wake up as expected, also no flickering. 

Then yesterday, I started the DDPM app again and sure enough, this morning only one of the monitors woke up while the other required pulling out of the power cord and plugging it back in in order to start working again.