Are insurance companies required by law to automatically renew car insurance?

No. However, the insurance codes of most states do provide that the insurer is required to give a reason for the nonrenewal.

Further, the state insurance laws, enforced by the insurance regulator, require that the insurer file, and have approved, "underwriting guidelines". These are the conditions under which the insured is willing to issue or to renew a policy. The insurance regulator determines whether there are "fair" (for example, they cannot be discriminatory and must comply with the law). If so, the insurer can make the policy issuance/renewal decisions based upon them.