I can only speak to a pair of audio technica headphones where I disassembled to repair a similar problem - within I found a lot of carefully shaped pieces to control how far the cup could pivot or stops to prevent flexing too far...it's was all too intricate and complicated to reinforce. All super-glue attempts quickly failed - and/or finally glued in one spot. My final solution was to secure that side completely to the headband and let the other side pivot/flex to adjust. It wasn't an ideal fix - but as my head size only inflates/deflates (ego) but not physically it was a reasonable compromise. It did take some getting used to.

These all have a design flaw. I RMT'd my first pair after less than 3 months when it broke just above the right swivel. All four areas above and below the swivel points have stress cracks. The plastic is too thin. My 2nd pair, I wrapped many layers of plastic tape around all four areas to reinforce them and it has held for a year so far.