For safety reasons, when the utility is down so is your grid-tied inverter. This is to prevent the line workers from getting shocked as they repair the lines and restore power to all.
However, there is still a way to take advantage of the sun. By adding a battery backup inverter and a battery bank, you have basically added a UPS system to your house, with the added benefit of being recharged by the sun.
Depending upon your loads and the size of the battery bank, you cold operate in a limited capacity indefinitely. While you might not be able to run an air conditioner, you can certainly keep your food cold, a few lights on a night, recharge your cell phone, and maybe even run a well pump.
Contact Solar System Services for help in sizing your home backup needs.