I also have a similar issue ... but my guest is crashing/hanging randomly and not right after establishing the VPN session.
My host is Ubuntu 11.04 (64 bit) and my guest is Windows 7 (64 bit) ... running Virtualbox 4.0.8.
There's nothing special in the VBox log when the guest hangs and I have to power off/on the VM to get it back running.
When I'm not using AnyConnect, never had this issue. I have been experiencing this issue with the last 2 releases of Virtualbox (4.0.6 and 4.0.
but this might also be linked to when I upgraded the host from Ubuntu 10.10 to 11.04