Apple specifically instructs that the source computer be set by the user to never sleep before running Migration Assistant:
http://support.apple.com/kb/HT3231
"Avoid letting your source computer go to sleep while you are attempting to migrate.
To prevent your source computer from going to sleep during the migration.
- Go to System Preferences on the source computer.
- Click Energy Saver then select Custom in Optimization.
- Adjust the slider for "Put the computer asleep when it is inactive for..." to Never."
However the brand new machine (which is the DESTINATION computer, not the SOURCE computer) typically does not have any user account on it when brand new, so there is no way for the owner to tell it not to sleep. I do not expect this would be a problem normally because the DESTINATION computer is kept busy during the entire migration and hence would not go to sleep during the process. However there is a danger that the SOURCE computer could go to sleep, for instance while the DESTINATION computer is spending a lot of time moving files around or setting up directories, the SOURCE computer might have nothing to do for a long enough time that it might sleep which might interrupt the process. Hence Apple's guideline above.
I have used Migration Assistant and Setup Assistant several times and never had a sleeping problem, and these migrations took between 2 and 6 hours each.
Also, if you follow Apple's guideline and set the SOURCE computer not to sleep, that setting will get migrated over to the new one which means it won't sleep either.
I am guessing you had your source computer set to sleep and that's what it did, which caused the migration to stop, unfortunately.
If the Address Book is the only thing you are missing, you can manually migrate it easily. Their is an Address Book folder inside your user Library Folder, inside the Application Support Folder. That can simply get moved over to the new computer. Also, you may want to move several preference files from the Preferences Folder that have the name "address book" in their filenames. If you need to migrate a lot of other things also, then Kappy's suggestion is the best one.