There have been MANY comments about just this breakage and the plastic itself is indeed very weak. In every case Bose have stated that they can't (won't) repair and no replacement parts are available. Instead they only offer an expenditure of minimum $90 to upgrade.
Fortunately, I'm very handy when it comes to fixing things and I tested both superglue and polystyrene cement on the plastic. I have as a result used superglue on one side and poly cement on the other side.
Superglue has an advantage because once one application is dry, then additional applications can be added to build up a very strong joint.