Circuit that closes at certain voltage (as hotfix)
You could try to reduce the capacitance C2 and C7.
I suspect just for programming the noise on the supply voltage isn't that critical.

Remove the isolation.
Do you really need the isolator to program your boards? Can you do without?
Can you put the isolation barrier somewhere else, like the USB plug?
Or only bypass the power part.

Bodge a chip on it. Like the NCP361 Protection Controller.



The correct way is to use a voltage monitor. However I suspect your actual product requires this if it's this susceptible to supply problems. Not the test jig.