You may want to try an adjustment to see if it corrects this issue.
Turn the valve on.
Adjust it to the decreased flame position.
Remove the valve knob.
Take a very small flat blade screwdriver and insert it in the knob shaft.
Carefully and slowly turn the adjustment screw to increase/decrease the flame size.
All surface burners should be on and lit will making this adjustment.
After the adjustment is made,turn the burner hi and lo to make sure it stays lit.
If it goes out,re-adjust until it stays on.
I am still checking on your valve. There is a possibility all valves and manifold have to be changed out.
Source: Possessed Jenn-Air SVD8310S stove top