I imagine that as the problem has existed since I've had them

Dom,

 

Ahh, I see that the crack is between the power cord input hole and the exhaust-to-ear exit hole.  This is frequently caused by hot rock and roll tunes igniting in the chamber formed by the ear cup and the head.  Other causes include fast expanding red-ears as a result of third-round instructions from ATC or a minor navigation disagreement with your seat mate where you find you have inverted the GPS lat/long settings one hour earlier.

 

Have you considered JB Weld? If so, remember not to hold the pieces together if some JB gets on your fingers - it wouldn't be a pretty sight - fingers stuck to the cup and all.

 

Grayhawk