Cisco anyconnect keeps disconnecting and reconnecting

For me what solved this is to work only on wifi or only on wired ethernet connection (I disabled the wifi adapter (in Control Panel\All Control Panel Items\Network Connections in win10)

Now everything is stable!

I had the same issue and inspired by thedrs answer, I disabled all network adapters I didn't need for the VPN connection.

It turned out that the Hyper-V machine (and the corresponding virtual Ethernet adapter) I had running were causing it. After shutting down the virtual machine, no more reconnects occurred.