Is there a common reason for a Macbook battery to disconnect from the logic board?
It's option 3 - "Other."  There are two possibilities for your battery becoming disconnected with your logic board and both have to do with the molex connector:


The connector on your battery is broken/defective.  If this is the case, the warranty on the battery (provided you are still within the warranty) should get you a replacement and have this fixed.
The connector on your logic board is broken/defective.  If this is the case, the only surefire way to fix it is to have the connector replaced.  This will involve soldering of the logic board.





If repairing/replacing the logic board is out of the question and the everything works fine with the exception that the connector won't stay connected, you can secure it in place with some Kapton tape.  It won't be the most elegant solution, but for under $20 for the roll of tape, it's a much more cost effective solution.



As for your first two speculations...


Shocks. The amount of destructive force your Macbook would have to go through to "shock" the connector out would destroy your Macbook completely.  
Ejection system.  You would see some sort of mechanism to do this.  If your MBA senses things are getting too hot, it shuts the computer down.  There's nothing in any computer that "ejects" connectors.