Gary,
Thanks for sending me your files. They didn't include any crash logs, but after reviewing your log files I don't think you have any.
The only instance of a "lost connection" error was recorded on April 4. (If you want to to look further back, send me some older log files). Most notable is this log entry:
2009-04-04 05:16:21.946 -0500 #debug# VerifyCommand listeners probably dead, terminating process
It appears that the listener process (the Activity Monitor window) was simply running too slowly to keep up with the action's updates. The inter-process equivalent of the spinning beach-ball cursor.
What happens when an action is done is that it sends all of its listeners a message that it has finished. It then waits around for about a minute for those listeners to acknowledge that it's done and close their communications connection. If the listeners don't, the action process assumes that they died and just terminates. That's what is recorded in your log. But, if it turns out, the listeners weren't really dead, they may attempt to communicate with the action process again, which fails because that action no longer exists. This results in a "lost communication with helper" error.
Since I don't see any other errors or problems in your log, I'm confident that this was a harmless, and sporadic, communications failure between processes and not a failure of the verify action that was running at the time.