Oven "flickers" in power every now and then

This may be a device fault (loose wires, failing control panel, etc.) but it may be an actual power problem.

In the olden days, a short power outage - even a minute or two - made little difference to anything. Your AC-line powered clocks (whether in an oven or on the wall) would be a minute off and everything else would be "as it was before".

Now many devices, including ovens, have electronics that keep their state only if the power stays on continuously. This includes digital clocks (except the old "flip clocks"), computers, TVs and many, many other devices. They have "soft switches" that don't truly turn the AC power on/off, so that a circuit is running all the time that "knows" whether the device should appear to be on or off. Typically, a power outage of more than a second will turn all of these devices "off", so that when power returns they come back to a default state - typically "appear off" but in some cases "appear on" (e.g., many computers have a setting to automatically turn on after power is restored - crucial for servers, security systems, etc.) and in some cases give a power failure indication (like my Kitchenaid oven).

The big problem is on outages between roughly 1/60 of a second and 1 second. Almost any device can tolerate an outage of 1/60 of a second - one AC cycle. But handling more than that depends on the power supply design. Some devices will ride through several cycles quite easily. Some devices will not. I see this occasionally with failing battery backups (UPS). A UPS is typically designed to switch over to battery power in 1/60 of a second and for any low voltage (perhaps < 100V), not just a full outage. But if the battery has failed then the connected devices get nothing at all until power is restored, and can actually end up worse off than if they simply tried to ride through the outage on their own, particularly if the problem is low voltage rather than a full outage.

End result: If your incoming utility power has some very brief interruptions, you can easily find some devices resetting while other devices act as if nothing ever happened.

I bet that an electrolytic capacitor has failed inside of the clock's circuit and the clock has no charge storage to "hold it over" when there are short power interruptions that don't affect other devices that haven't malfunctioned that way yet (every appliance will succumb to this issue eventually, unless it's of extremely high quality).

The clocks in ovens and ranges have a tough life due to elevated temperature inside of the applicance when it operates. This causes premature degradation of the cheap capacitors used in such products. A properly operating clock will hold its time without issues when there are short power interruptions of under a second or two. If it doesn't, it's a clear indication of a problem. Some clocks may be so poorly designed that they barely maintained their time for a fraction of a second, in which case they have to have their filter capacitors enlarged in value compared to what the cheapskate manufacturer put in there.

With a modicum of know-how this would be a very easy thing to repair, but it'd help to be able to measure the capacitor's value after removing it from the clock to confirm the diagnosis. It can be replaced in any case - it won't make sense to put the old one back once it was removed from circuit as needed to check its value. The replacement should be purchased only from a major electronic component distributor (like DigiKey, Mouser, Newark, Avnet, ELFA Distrelec, etc. - not ebay nor aliexpress!), be rated for 105degC operating temperature or higher, have a rated life of 10,000 hours or more, and have the operating voltage and capacitance ratings equal to or greater than those of the part it replaces. It's extremely unlikely that said capacitor will ever need to be replaced again during the useful life of the appliance.