Honestly, with various systems (Not just Zimbra) which send me messages I don't need (and some I do) I just setup mail filters for them. For example, I have filters for my backup software that route all messages except those with ERROR in the subject to a 'Routine Notices' folder. Messages with "ERROR" from the same software go to my Inbox as normal.
You can do the same here. Filter messages with the body containing "Service status change: gates.unicorn.kiev.ua mailbox changed from stopped to running" in the body to another folder (or even Trash if you want).
Not the same as stopping the messages, true - but it does filter them out so you don't see them.
State University of New York at New Paltz