Once the Apple ID have been "registered" and is listed in the iMessages account pane in the Messages Preferences it should not need to be entered again.
However there is a sort of "known issue" with Messages reaching version 7.0.1 with the OS X 10.8.2 update that needs the Mac's Serial Number to be present (It is normally read in System Information or in the About this Mac pane (click the current OS line twice).
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Mountain Lion 10.8.2)
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