Lost hot wire from the utility
Call the utility emergency number and report an outage. They'll have a truck out in an hour on a Sunday.
And it's random rooms. No power in 1 upstairs room, but power in the other two. No power in main room of basement, but power in laundry room and bathroom of basement.
Not random at all! I bet if you identified the breakers of the circuits that are out, they would be on every other row of the panel, like described here.
The power will go out for a random period of time, and then come back on for a random period of time.
Not random either. That is your tanked electric water heater, or other 240V load, cycling on and off.
A water heater and any large heat load is just a giant resistor between the two hot phases.
If one phase is dead, then it connects the dead phase to the live phase through the resistor, causing it to re-energize. Like borrowing electricity from your neighbor through way too many extension cords lol. So modest 120V loads on that phase will now power up normally. Greater loads on that phase will make the voltage sag considerably.
But here's the weird part, the current moving through that resistor is heating the resistor. Modern water heaters are so well-insulated that they have very little loss. Even this limited current is enough for them to "get ahead" and eventually reach their target temperature. And then, they turn off! Cutting power to those appliances. So this (or another similar heater) would explain the random power-ups.
Turn off the breakers on all your 240V appliances (which you should do anyway, as this isn't good for them). If the sporadic appliances are now dead as a doornail, that was it.