@necrochaos,

I found this in our documents:

"Check whether set block ICMP from LAN port: Login the WEB interface, go to Advanced->Security->Firewall. We will block the ICMP from the different LAN subnet as default, so if the customer doesn’t check it, it will block this session."

I also am assuming that you are not using the VPN features on the Router, and simply accessing the VPN server through your home internet.

When you are disconnected from the VPN, try looking at the logs on your router to see if there is anything that could indicate where the disconnect is originating from.

  @necrochaos,

Try taking a look at your system logs, there should be something that could indicate the cause of the disconnect.

  @necrochaos,

If you're not seeing anything, it means that there is most likely no kind of disconnect occurring from the router side, rather it is an issue of a blocked connection. After searching around a little bit this seems to be a common problem with the AnyConnect Application and Service, it seems that there are tons of potential solutions revolving around closing ports or services on your computer.

A lot of threads even say that having a computer with two types of network connections, wired and wireless, can cause the issue.  Others indicate that the use of IPv6 can interfere with the connection. 

I would recommend looking to see if you can disable any virtual or extra network adapters from your computer.