In many (maybe most) SW radios with IF chips the threshold where a radio will stop on a channel is set in the IF chip itself, or sometimes by the IF chip in conjunction with an outside component used as an adjustment.
The threshold level can usually be found in a datasheet for the radio's IF chip, usually expressed in dbvu or uV.
It's possible that this threshold could be adjusted in some radios by changing out a resistor, but you'd have to a) look at the datasheet for the IF chip, b) look at the schematic and know what you're looking for (i.e., have a real good understanding of the circuitry). And remember most modern radios are surface mount. :-(
And also remember that unlike VHF, on HF you have static crashes, variable noise levels and such and if you could actually set the automatic tune threshold lower it may be counterproductive, i.e. it may stop on noise and static instead of actual SWBC stations.
One 'trick' I found -- at least with one of my radios -- is to watch the tuning indicator LED. Sometimes the LED tuner indicator threshold can be lower than the auto-stop threshold. The radio will tune past a station, but the LED will light up, showing a medium strength station's signal was just passed by.
In the radio I'm referring to, a Realistic DX-375, the tuning LED will often light up on a station that is just below the auto-stop threshold. I just hit the tuner button when I see the LED light up, and back up a channel or two and see what's there.