Anyone run into this???

When I put a large bit in my drill press, even going very slow the bit
stops in the wood and the collet lets go from the press when I raise it
up. So...the bit (a 3 1/2 Starrett bi-metal hole saw bit) stays in the
wood. I tried another bit (A large Dewalt forstner) and same thing.
The chuck won't stay in the collet.

I turn off the press, lower the press onto the tapered piece and the bit
will lift out of the wood. I tried removing the bit and then pressing
the chuck very hard onto a piece of wood to try and set it, but it does
the same thing again.

Keith P