Hi,
As I have used Messages more and more since the Thread was started it is becoming clear that I too am suffering with similar issues.
I tend to keep my Mac Off when I am not using it.
I tend to be here, for about 3 hours of an evening.
If I have been iMessaging my wife from my iPhone during that time it rarely syncs when I turn the computer back on and start up Messages.
I have recently been testing to help some I knew through using AIM originally.
I can send from my Mac version and his iPhone sees it.
He can send from his iPhone and I see those iMessages on my iPhone and my Mac - except for those he send when the Mac is Off.
He cannot send ( at least not continuously) from his Mac to anyone.
While his error seems to point to the iMessages server not keeping the link between his iPhone Number and Apple ID it does highlight the on-going issues with the Mac's Messages app's integration with the iMessages service.
I would still recommend using http://www.apple.com/feedback/ichat.html to provide Apple with the feedback they obviously need.
I tend to still use this page as Messages is iChat+ and continues the Numbering sequence that was being used.
The page lacks the Variations for iChat 6 or Messages (version 7 and 7.0.1) so you will need to eneter the detail in the Free text area.
8:52 PM Monday; May 20, 2013
iMac 2.5Ghz 5i 2011 (Mountain Lion 10.8.3)
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
"Limit the Logs to the Bits above Binary Images." No, Seriously