What can you do when your insurance company raises your premiums due to a hit-and-run accident when the at fault person can't be located?

You could appeal it, but you probably wouldn't get too far. That's why it's so important to pick a good carrier before you have an accident. Slightly higher premiums pay off in the long run; many "cheaper" insurance companies will pretty much abandon you after there's a problem. But see if you can appeal to someone higher in the company than the department raising the premium.