Hi,
First off.
The "Sync" as Apple calls it is only "Display on all Devices" and nothing more.
Deleting it on one device will not delete it on another.
On the Mac the iMessages are stored in ~/Library/Messages in file called chat.db with a couple of supporting database items alongside.
If you "close" or remove the chat in the list in the Messages window (the x when you mouse over the name and pic) then the iMessage will "return" as an "Aid Memoire" to the previous conversation.
This is local on your Mac and is nothing to do with any 'sync' over the iMessages servers.
The longest time I have experienced was using my iPhone on a hotel WiFi on a Friday evening away form home and picking up those same iMessage on Sunday evening when I turned my Mac on.
The iMessages servers "push" the iMessages to the devices it thinks are Registered.
However this only happens once. When the device has the iMessages the servers stop sending it.
This is to stop what you seem to describe - the endless attempt to delete the same iMessages.
It is more likely you are talking about the "history" feature.
9:56 pm Friday; February 7, 2014
iMac 2.5Ghz 5i 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad