Hi,
On the Mac version what tells you it has Stopped working ?
Have all Contacts you have tried go red and say "Not Registered with iMessages ?
Or when you send something is it immediately marked "Not Delivered"
If either of these are happening to you then the Mac is not logging in properly to the iMessages Servers.
You will need to Contact Apple Support and state you have an Apple ID issue (Free to fix).
Even then there can be a lot of hoop jumping for them to be convinced that it cannot be reset from your end.
Politely insist that the iMessages Servers is reset with regard to your Mac's use of the Apple ID.
Even at that point they are likely to tell you that it will take 24 hours to reset.

8:45 pm Wednesday; February 17, 2016
iMac 2.5Ghz i5 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