A recent patch to Internet Explorer (KB3021952) has broken Cisco AnyConnect v3 on Windows 8.1. I'm not able to test v4 as we don't have access to it. It looks like the concept of on-line\offline working has disappeared causing AnyConnect to become confused and believe that it is permanently offline.
The message I kept getting said that the VPN susbsystem was unreachable.
The article below mentions a registry change, but this didn't work for me. The comments suggested running the GUI part of Cisco AnyConnect in Windows 8 compatibility mode, and this indeed did work for me.
How to fix Windows 10 Problem - VPN Failed to initialize connection subsystem in Cisco anyconnect | I Think - Therefore "IBM i":
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