In the eyes of insurance companies, if your tenants claim loss severla times through their renter's insurance, your property must have some faults. Therefore it increases their risk and of course demands high insurance premium.
Two points learned this experience:
1. Insurance claims not only attached to the person who files the claims, but also attached to the property address. If your tenants have renter insurance, ask them to notify you before filing any loss. For small loss, you would rather pay for their loss, instead of causing big troubles for your insurance renewing.
2. When you buy a house, please make sure the seller did not file several insurance claims recently (within 3 years). Otherwise you may have trouble to buy insurance for this property.
3. Smilar to your credit score, everyone has an insurance score and each insurance company evaluate their risk based on your insurance score (they share the database). The red flag for them: 3 claims within last 3 years. Try not file small claims. Sometimes this is bad in their eyes, even if you call them to ask for the claim question, then decide not to file the claim. They think you have high risks.