Power plugs in train repeatedly turning off

As already suggested by Gagravarr, when the train is coasting through a neutral section, all non-essential power is turned off. You might notice some lights and air conditioning being switched off. If you're near the engine you might hear some telltale clunks and noise variations when the engine is switched off and back on.

This happens for a brief time in some places where the train is switching between isolated sections of the power feed, including switches between voltages (France has multiple electric standards, see e.g. this map. This also happens sometimes for a longer time on certain flat or downwards stretches of track between stations, to save power.

If that's the explanation then it would happen mostly in the same places, but not systematically (if the train is late it'll keep the engine on to catch up) except for power feed switches.

It's impossible to know for sure that this is what you experienced, but it is a likely explanation.

I had this happen on airplanes because my laptop was drawing too much power and resetting the breaker. My solution was to use my laptop on battery, then close the lid and plug it in to charge when I wasn't using it - such as when I was eating. In this way I am able to keep the battery reasonably full, but not keep tripping the breaker. (There is a lower draw from just charging than from charging and being powered up.)

If you think this might be happening, try plugging in something with a much lighter draw, such as a phone charger. If it still resets after 20 minutes, it's not related to your load. If it does not, then you can try only charging when the lid is closed or other draw-reducing techniques.

I can't actually find out how power on trains works, so I'm going to assume it's coming from either the rail system electrification, generators, batteries or some combination of them.

In any case the power from whatever source(s) is going to need to be converted and adjusted to get the 230V AC that things expect from a power socket. Unfortunately this is a non-trivial thing to do in a train where (I assume) the incoming power is probably not that stable.

I'm guessing that what's happening is that the power available from the socket may be dipping below the minimum power required by your power brick. Or, because you think it's cyclical, perhaps the AC cycles are not quite synced and it drifts over time eventually causing your power brick to stop recognizing it briefly. It's also possible that something is periodically drawing power from the system forcing it to dip under a usable power level.

Sadly this means that there's unlikely to be a some special socket where you can avoid this.

It is possible that using an expensive surge protection / power filtering extension cable might smooth out things enough to keep it running. But without debugging exactly what's happening with the socket there's no way to tell.

If your problem is just the screen dimming then I suggest you go with the option of changing the settings. It depends on your device and OS but you may have the option to delay the dimming for a few minutes (which wouldn't really be too much of an issue at other times). Or many PCs have options to save multiple graphics settings and switch between them easily (often with a hot key).

Failing that there are third part tools that can do it, if you travel at regular times you could even fully automate it based on the time of day. I'm getting a bit off topic for Travel here but, if you're technical or happy with a bit of a learning curve, I'd check out AutoHotKey.