We've had our first couple weeks of this in game, and already I've heard "Be right back, Tornado," from some guildies living down in Kansas. Luckily everything was okay and no one got hurt, but the fact still remains – we lost our head Mage for 30 minutes, and that's 30 minutes of our life we can't have back!
While a Mage having to take a break in the middle of raids isn't a show stopper, having the main tank (my role) go offline is. I've had the unfortunate situation of having that occur a couple days ago. The computer I was raiding on wasn't plugged into my UPS (Uninterruptable Power Supply), so I was disconnected from everything when we lost power for about 30 seconds. However with a bit of tinkering around, I was able to put myself in a situation that lets me stay on even when the power hiccups.
What I was able to do was to plug into the UPS only the essential things my main computer needs to stay online. This included my CPU (the big box where most of the computer's hardware is stored), my monitor, my cable modem, and my router. That filled up all four spots available on my UPS. I tried this quickly one evening when the power went out early on. When it went out again later that evening, my other computers got cut, but the computer I was playing WoW on kept going – along with the internet connection.
The UPS had enough juice in it to keep going for the 30 seconds the power was offline, and luckily the cable system didn't require any local (to me) power to operate beyond my cable modem and router. So if you're in an area that has lots of storms and power fluctuations, I highly suggest you do this if you don't want your group-mates yelling out in frustration every time a storm passes by.