Well, in fact, ashServ.exe never asked me to connect…
Maybe Sygate is monitoring the local access of it to your own HDD.
So, of course, ashServ is trying to scan something each 1 minute.
I’m just trying to say that your Sygate configuration could has some problem because it’s monitorin local connections and all programs have local access. Maybe some configuration of the local network ???

The program that must connect are avast.setup and ashMaisv.exe.

Go to Control Panel > Add/Remove programs > avast! antivirus > Remove
Then choose Repair function in the popup window (Repair).

If this does not help, can you uninstall / boot / install / boot again?