Capacitor behavior in oscillating circuit
You're probably not misunderstanding how a capacitor works. It's probably the programmable unijunction transistor that's acting weird.

My understanding is that a PUT stays on as long as the current through it is greater than a certain threshold. Since you decreased R1, I bet the current when the cap is discharged is higher than that threshold, so the PUT never quite turns off.

Try changing R1 back to 470k and see if it works. (It will be a little tedious to test.) Then you can decrease R1 and see how far you can go while still having the PUT turn off.