Hi Rob,
I have had the same problem with my inherited drill press. It must be
at least 70 years old. The chuck come falling off at inopportune times,
usually when cutting with a big drill. I looked for burrs found none,
cleaned the surfaces completely and still had the same problem. Finally, in
an act of desperation, I put a little valve grinding compound on the chuck
taper. I held the chuck against the mating part with the drill rotating.
After a minute, I cleaned the grit from the shiny surfaces. Reassembled
with oil and it has been fine for over a year.
Good luck,
Dave