It would be so much more useful if we could have this conversation on the openconnect-devel mailing list.

The 'dead peer' message above means that the server did not respond to our 'ping'. The HTTPS connection to the server seems to have stopped working. When this happens, openconnect should *reconnect* to the server. Does it not?

Can you run tcpdump (filtered for port 443 on the vpn server) and show the traffic while this happens? And show the output of '/sbin/route -n' while you ought to be connected. Please don't post them here; send mail to the openconnect-devel@lists.infradead.org list.