AlexZulu: It's an internal ribbon cable that is rather fragile. It connects the speaker assembly to the logic board.
So far, I've noticed two potential points of failure with this design. It's a "folded" ribbon cable rather than a flat one, and the two folds in the narrow space of the original MBA case can get crushed and cause non-visible damage to the cable's conductivity. This may be because the original MBA design was not entirely rigid. The case bottom has some flexibility to it.
The second point of failure is the contacts on the logic board and sound card themselves. Instead of an interlocking jack they used a design that can loosen, weakening the connection. This hypothesis seems to be supported by the fact that, if the audio flex cable (as it's called) is not actually damaged, unseating and re-seating the connectors on both ends can sometimes restore functionality. But over time, the connectors themselves can wear from too much wiggling.
I'm puzzled as to why they ever used this design, but I suspect it was revised in later versions as when the unibody MacBook Pro's came out, they seem to mostly use use flat internal cables with interlocking connectors that snap tight.