On Wed, 15 Feb 2017 11:44:52 +0000, GB wrote:

Am I understanding this correctly, the only thing holding the chuck in
place is that it has a tapered shank that fits in a tapered hole?

Yes, expect the hole is in the chuck and the spindle has the shank.

I have a similar cheap pillar drill, chuck does very occasionally
fall of.

The OP does seem to having serious problems, where is the drill kept
has it got damp and a bit of corrosion happened in the taper? Tried a
bit of Plus Gas or diesel applied to the joint? Tried banging the
chuck harder on to break the bond?

--
Cheers
Dave.