Here are five suggestions: 

• Clarify why the company won’t renew your policy. The letter should identify the cause and your agent should be able to help clarify.
• Ask your agent if there’s a possibility of appealing and reversing the nonrenewal. For instance, let’s say the company is nonrenewing because of tickets and claims activity, BUT two of the claims were caused by your son, who has since moved to another state. Ask the agent if you can appeal based on the new situation.
• Meanwhile, explore alternative options. Independent agents will tend to be in a better position to help you because they will have more options and some companies are more flexible. Nevertheless, the reality is that a new policy will likely be more expensive until the claims or tickets start to wash away with time.  
• Be up front about why you’re needing to switch to avoid false starts. Although it may be tempting to hide claim or ticket history, the agent will not be able to give you accurate or realistic options without good info. And ultimately, the insurance company will check that info; so, better to be upfront about it. 
• For your new policy, consider increasing your deductible to $1000 or more if smaller claims were a part of the reason for cancellation. Then, you’ll be less likely to file another small claim while remaining protected against a big loss. Plus, you’ll save some money while you wait for time to pass.