I suspect that the urge to hang onto things that are valuable to you is stronger than the urge to hang onto a couple props at a stage, especially when you are not really surprised by the buzzer going off.
Some years back on another gun a fellow (coincidentally from Indiana) recounted how when he came home from shopping at the grocery store he surprised two burgers, and himself, in his apartment.
He later realized that he automatically shifted the bag of groceries from his right arm to his left arm, THEN drew his pistol. He didn’t even think about putting down the groceries until the burglars had hightailed it out if there.
One of my NCOs injured his knee trying to save a computer monitor he was carrying when he stumbled walking up some steps. Although intellectually he knew that the monitor was old and simply going to DRMO (to be sold as surplus), his ingrained response was To not damage the monitor while trying to recapture his balance.
Even not under total duress it happens. I was at John Murphy's class last year and discovered under stress/rushing I failed to drop my pepper spray when I transitioned to my pistol during a drill. I ended up holding on and getting a **** poor support hand grip.