I don't know the answer. Are they all using the same Live ID for Mesh or are the folders shared between LiveIDs?
What OS is the machine running? Are all 3 machines on and online at the same time? Are they all on the same LAN/ Is there a 3rd party firewall in place? Is the problem PC in heavy use for other purposes?
If the 3 machines are using Vista or Windows 7, you should consider switching to Windows Live Mesh, part of the just released WIndows Live Essentials 2011 as this beta will be ending at some future date.
If you are going to continue running Live Mesh beta, I'd consider reinstalling on the problem PC if you can't determine the cause of the issue.
-steve
~ Microsoft MVP Windows Live ~ Windows Live OneCare| Live Mesh|MS Security Essentials Forums Moderator ~