What would cause this?

[brino]

Even if your lathe is missing the feed chart, it is likely using standard gears and lead-screw, so in the short term it's likely not too much work to find a photo of a feed chart from a manual or from another owner.

How hard would it be to connect a stepper motor to turn the long threaded drive rod? All I'd need is an inductive pickup on the spindle to measure drive RPM, coupled to an arduino controller and a stepper motor driver, and I wouldn't have to worry about working some sort of witchcraft with the fragile (And already quite chipped and worn in some places...) Gears. What do you think?

That would be a fun project.
If you do tackle it I sure hope you share the progress and results here!

-brino