There will be a way for you to override your firewall without lowering your protection system-wide. You need to create an exception for either the FTP protocol or for the Sentinel program. I think FTP is the better way to go. Without knowing your firewall program and setup I can't help further, but you should be able to take it from there.
I just purchased a HomePatrol-1 and was having the same issue. Was able to ping and traceroute to ftp.homepatrol.com successfully. Was running Sentinel as administrator. Tried creating firewall rules for FTP and Sentinel. Disabled my anti-virus program. Nothing worked.
However, I typically use a VPN. When I disabled the VPN, both the firmware and database updates worked! Is it possible the FTP site is blocking a range of IPs?
Anyway, I hope this helps someone else in the future having the same issue.