Your insurance company can cancel your policy at any time if you violate one or more of its guidelines during your policy period. Same goes for non-renewal. Things such as failing to pay your premium on time, losing your driver's license due to suspension or revocation, submitting too many at-fault claims, or misrepresenting your driving history or past insurance claims could all be reasons for cancellation or non-renewal.
In either case, your carrier must notify you in writing within a timeframe legally required by your state. When it comes to cancellation, your insurance company is required by law to state the reason, not so with non-renewal. If you want a reason but aren't provided with one, you must send your insurer a written request. If you believe you've been unfairly treated, you may have legal recourse through your state's department of insurance.
And don't forget about your "binding period," the time when your insurance company is especially conscious of your risk level. The binding period usually occurs within 60 days following your auto insurance application. If your insurer finds a discrepancy on your application, on your driving record or with your credit, it can cancel your policy.