Drill Press Chuck taper is unreliable

[reogaro]

The big drill press or its drill chuck have a problem, the taper doesn't hold and the chuck keeps falling out. The wood turning lathe had a identical chuck so we swapped them around, please comment if that didn't fix it as that would mean the drill press taper is the problem, not the chuck.

And when using the wood turning lathe, be careful as the drill chuck taper might not hold and release the drill chuck. Please comment if that happens to you as it would point towards the chuck being bad.

I have marked the potentially bad chuck (placed in the woodturning area) by taping a white piece of paper to it.