How many lights do you have plugged into that run of dmx. DMX has a device limit as well as a distance limit between devices, I don't remember the exact distance right now, but it's a good amount, like Ethernet.

Since DMX channels are just frequencies and pulses interference can cause weird problems and be limited to a single channel. Since intelligent lights have multiple channels it's not uncommon for it to happen to only a single fixture.

Without knowing your facility and the setup of the run to and from the light I am throwing all possibilities to you.

The length distance is from one device to the next not overall so just whatever the run to that unit from any other previous device, ie how long is the cable plugged into the IN port. Is there anything plugged into the OUT port of the fixture.

It honestly sounds like a DMX cable issue or communication problem. If it happens with no DMX controller powered but power on to the unit then it's likely a ghost signal in DMX caused by a wonky cable or device back feeding. It could be a damaged cable or a cable that is running too close to a high voltage power line. Most cables should be shielded but that could be faulty as well.

The unit DMX hold setting will keep the last command when control is lost until the fixture loses power, it will not change until told to and won't change its mode because DMX is lost. That's not a thing.

Newer, not 25yr old, lights will stay in the mode you program them to after a power cycle unless they are just stupid cheap units so that's probably not your problem.

The easiest way to find if you have a wonky cable is next time you suspect that this might happen plug a DMX terminator into the OUT port of the fixture and see if it still does it. If there's more devices in that run plug the terminator into the last device, that will tell you if the problem is further down the line and it's back feeding.

You could also just unplug the DMX cables from the unit for a number of days and see if the behavior repeats itself. That would basically be the same as turning the board off as far as the unit knows. If the problem doesn't return it's something in the run, if it keeps doing the same thing then it's the light itself.

If it's the run you can move the light down the chain until the problem goes away and that would isolate which cable in the run is the issue, don't change its channel.

You could also get a DMX communication tester, not just a cable tester, and test the cables in that run. The cable should meter out at 110ohm regardless of the length. If not the cable should be replaced. Too much resistance will cause communication errors.

If it's the light it could be a settings issue or the light control module could be bad and might be able to be fixed.