It depends on what you mean by "dropped". There should not be any gaps for your auto insurance. Otherwise, it may raise a flag for the new insurance company. Besides, if your insurance company did not renew your policy, you should always find a new insurance company without creating a gap.
The information in this answer is general in nature and is not legal or insurance advice for your specific situation. Policy language varies carrier by carrier; your declarations page is the final word. If you're unsure, call your agent before you need to file.