If AccountEdge quits as soon as you launch it with the message that "AccountEdge Quit Unexpectedly" this can sometimes be resolved by deleting a specific file.
This will often happen because you have had hardware replaced or you've migrated to a new machine.
To resolve this issue:
Open Finder
Click Go > Go To Folder from menu bar at the very top of the screen
Enter ~/Library/Application Support/Acclivity
Delete any files that end in .plist (ex: AccountedgeneLicenseUS20.plist)
After deleting this file the software should open and will ask you to Register.