In mdaemon, exchange, we used "Networker server" to backup our server, didn't need to stop it. Now I think if we do the same with zimbra server.
I found a program, backupPC, which can use for backup server linux(I think it can backups when server still runs). But I've not try it yet. Anyone has an idea for this solution? Because, I think with a server the important thing is must always online, but with zimbra FOSS edition we must stop it (too bad)
I'll try it and report to here