Broken battery base in Macbook Air 13?
I see this in MacBook Airs, and similarily in MacBook Pros (2012 and earlier non-retina), all the time. It is in my judgement simple material fatigue.

The battery in the MBAs are held down with 5 screws, in MBPs with 2 or 3. The retainer plastic around these screws are thin and therefore relatively weak, which means they are prone to breakage due to mechanical stress. They are stressed from the downward screw pressure, and will get additionally stressed from the bumps happening in normal use, which will induce a mechanical force on the battery relative to the screws. There is nothing more to it. The temperature in these, especially in the corners of the MBAs, do not rise enough to cause the plastic to become brittle.

This breakage might have been a contributing factor to why Apple has switched to holding the batteries in place with glue instead. I have seen a couple of instances where a piece of this retainer plastic has come loose and lodged itself in the CPU fan, stopping it cold.