Quantum,
Firstly, Zone Alarm should not affect ashserv.exe
ZA can prevent Avast from accessing the net, but will not shut down the exe.
Sometimes, "glitches" arise in a system without being present in another. ONLY if the problem persists throughout the user community will it be necessary to take an indepth look at logs and such.
Right now, it is my feeling that the two of you suffered a user "glitch", nothing more.
and also.....If you are having the same problem as another user, then please post within the same thread. It makes this easier to follow and takes up less room on the forum.
Glad you like Avast.