I don't see any connection between the two services. But, if really someone is sending too many requests to your MX on port 443, (based on what they are doing), your MX may run out of memory and eventually panic, which would explain AnyConnect Restarting and ports are flapping. If this is true, you shouldn't hear any complaints this week since you are using a different port. Also, you may set AnyConnect to use port 443 again but connect a switch between your ISP and the MX to mirror the uplink port of the MX and check what kind of traffic is sent to the MX on port 443. Please let us know what you find, this is really a strange problem.
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