That's always a worry, and one reason I went with a diesel genny as diesel stores better for longer periods. I put Sta-Bil in mine and keep the tank full. Also, I believe the local Co-Op has its own generator, so as long as they an get fuel, I can refill, although in real emergency, even that would be at a premium. The big fear out here isn't so much wind or ice storms but an earthquake, and if we got a bad one, all bets would be off, along with the power.
My battery backup system can run the house for about 5-6 hours if I'm careful, so I figure I can keep the house running for about 7 days on the fuel I have on hand.
The worst power outage we've had here was 84 hours after a wind and ice storm a couple of years ago and I weathered that just fine.