When can an insurer cancel your insurance?

It depends on your state and company. Some can non-renew you for filing too many claims some can do that if you live in a territory where they no longer want to have a certain exposure, like living on the coast and not wanting to have the same exposure to wind or hurricane damage. In some states it is very hard to non-renew an insured and the insured has to have a certain number of state "points" before you can non-renew.