@Condensate 

The router should not filter or cut any VPN connection as it has the VPN passthrough. If anything you could make sure the feature is enabled (Advanced > NAT Forwarding > ALG).

@Condensate I am having the same issue with my A7 router.  I just purchased this over the weekend and today is my first day working from home, attempting to connect to VPN through Cisco AnyConnect.  The VPN can be established, but within 20 seconds, it disconnects, attempts to reconnect, connects, and go through the cycle continuously.  I don't have this issue if I connect directly to my modem.  I am using a hardline connection from the router to my PC.  I wasn't having this issue on my previous router.  All of the settings on the router have remained unchanged from factory defaults, except that I updated to the latest firmware after install.

@RobertEC 

Here is an older thread of users that had similar issues: https://community.cisco.com/t5/vpn/anyconnect-vpn-session-disconnect-and-reconnect/td-p/2474657

To see if it may be something related to the router firewall you can add your computer to the DMZ, then test the VPN connection. Disable it when you are done testing.