Escrow account to pay hazard insurance

I did a refinace last month and the new mortgage is FlagStar. I have an escrow account (for property tax and hazard insurance). This bank is a trash and I can never get hold of anybody to talk. I reminded them several times before the due day of insurance to pay through email. They still didn't pay and I got a cancellation notice from insurance. Can I hold the bank liable for any loss if something bad happens during these period with no insurance?