Connectify doesn't work with my Cisco AnyConnect VPN
Unfortunately, Cisco recommends not running Hosted Network (this includes Connectify, Virtual Router, etc.) at the same time as Cisco AnyConnect, which Cisco now calls Cisco Secure Client. Cisco gave this advice under 'Avoid Wireless-Hosted-Network' in its AnyConnect release notes.
Connectify Hotspot 27 creates its hotspot with Wi-Fi Direct by default, and uses Microsoft Hosted Network only if you switch to it under Settings > Network > Wireless, or if your Wi-Fi adapter supports nothing else. We haven't confirmed whether Cisco's advice also applies to Wi-Fi Direct. See What is Wi-Fi Direct?
If you need both, use them one at a time. We apologize for the inconvenience.