I would just leave it on. The motherboard doesn't really use than much power when powered down. It sounds like the wireing in your house/apartment isn't suficient for the number of items drawing power off it. I had a fire marshal (inspecting the apartments I live in) tell me that it is not uncommon, especially in older buildings, for the wireing to be insuficient for all the electrical devices that people use today. Basically there is too much draw on the wires. You are literally sucking power out of the wires faster than they can deliver power which causes the power to drop momentarilly. You see the same thing with high power car stereo systems. the power demands are so high on a heavy base hit, that the wires delivering power to the amps cannot feed power fast enough, so you use a capacitor (a BIG one) to buffer the power. Your system/power supply takes a lot more power when it first starts up which is what causes it. If it continiouslly pulled that much power it would probably be a fire hazard (though your breakers should trip before that happens). Luckilly it is only momentary. I'm not sure if there is any kind of a capacitor device for household current (I have never heard of one but that doesn't mean they don't exsist), but maybe an uninterupted power supply would help buffer the power when it starts. Also be aware, if other high drain devices like your fridge or washer cause this, and your computer is on the same circuit, it can cause stress on your computer. In therory, a power supply is suposed to take care of these power drops and a good quality one can to an extent, but they can only do so much. If there is not enough power then there is not enough power and the power supply cannot create power to even it out (it should have capacitors in it that can do it but only to a limited extent.
An uninterupted power supply has a battery that provides the power to even out power drops. My uninterupted power supplys would trip and go to battery backup momentarilly every time the washer or drier came on. I now have the computer in a diffrent part of the house and on a diffrent power circuit, and don't have that problem anymore.
An uninterupted power supply might be a good idea, and if moving the computer or maybe running power from a diffrent outlet is an option, then you can hook it up to a circuit that doesn't have other high drain devices (washer, drier, oven, fridge, airconditioner/heat, home entertainment system etc). Just shut off your circuit breakers one at a time and see what all looses power on each breaker (including the wall sockets). Also, look at the ratings on the various breakers. You may have some circuits in your house/apartment that are designed for more current.
Your power supply has protection from crashing the computer when this happens. The motherboard doesn't actually power up the system till after a brief delay after the power supply powers up. When the power supply powers up, it waits to detect that power has stabalized and then it sends a power good signal to the mother board letting it know that power is stable. This doesn't help you if the computer is already on and something else causes the drop in power though.