I checked on my PC and found a couple things.
1. There was one active log file and two archived log files (dates appended to their names). All were 2KB in size.
2. When I ran CCleaner, it removed the two archived files leaving the one active file. Of course in CCleaner I have the option selected to remove the ZA log files.
The contents of the log file are going to have to be examined and, like the recommendation in this topic: http://forums.zonealarm.com/showthread.php?t=72436
its probably best to contact tech support and give them the details of the log entries (read the last 2 posts).
Based on the comparison to my log file, I would say that 400MB and climbing is not normal.