Have run into insurance issues with kit-cars in the past. In California, they may not refuse insurance on ANY car that's legally registered, however some of the agents try the "it's not in our database, we cannot insure it" excuses. However, just because they must provide insurance doesn't mean they want to, and it may not be cheap.
Things for you to check are, firstly are they allowed to just cancel the insurance contract (or were you at the renewal period.)
Secondly, are they allowed to refuse you coverage (check with your state insurance commissioner.)
FYI, I use Farmers Insurance.