How Often Should You Search
Your homeowner's insurance is usually paid annually. There's little benefit in changing before your anniversary date, because you will not get a dollar for dollar credit. For instance, if your annual payment is $500 and you have paid $500 and want to cancel after 6 months, you will not be guaranteed the entire $250. You're aware of fees, etc.
It's best to check and decide at least 6 weeks before your anniversary date because some insurers manage to get their money out of your escrow account before the anniversary date (if you have an escrow acct.)
If you find less than a $30 difference between the nationally known companies, then it may not be worth the time and effort of changing. Be sure to compare apples with apples. Coverage differences are easy to spot, however, things like getting a benefit for having an alarm, or a dog, or a fire hydrant nearby are internal decisions on how much to charge you. If the company that insures your auto also has your homeowners, you may get a little lower cost. If it's a lesser known company, there's no way of guaranteeing that a low rate today will still be a low rate for the next 2+ years. It could have been a teaser.....