Typically when an insurance policy is issued the insurance company, such as AARP, cannot cancel it except for reasons specifically listed in the policy. Normally state laws limit the reasons insurance companies are permitted to cancel someone's policy. Such reasons can include non-payment, misrepresentation or fraud by the applicant.

Most states do allow insurance companies to decide at renewal time if they want to discontinue a person's policy, again except for reasons that are forbidden by state laws. If a policy is not renewed typically an insurance company is required to give a written notice at least 30 days before the end of the policy period to give the person time to find new insurance.

Since each state and each insurance company has its own rules for the cancellation of car insurance policies you should check with AARP directly to see what reasons they state they can cancel a policy for. To get your state's governing laws for this check with the insurance regulatory body of your state.