Michael Koblic wrote:
I tried to drill a 3/16" cross-hole in a small steel cylinder (0.3125"
diameter,
0.400" length).

(...)

Any other explanations or suggestions?

I conjecture that the material is work hardening.
What would happen if you used a stub length drill,
pecked, and (importantly) used more feed pressure
on the quill?

Think Cole Drill Mode.

--Winston