Compare the 135v converter shown on page 23 of the datasheet to the -120v converter shown in fig. 2 of Jesus Rosales' Design Note 545:
I built both designs. The 135v converter works, but the -120v converter doesn't run at all. Of course, I didn't faithfully implement the schematic of fig. 2. :)
1) I left the Sync/Mode pin grounded, rather than connecting it to the IntVcc pin.
2) The SS cap is still 0.2, rather than 0.22
3) I omitted the 10 ohm resistor
4) I used standard high voltage diodes, rather than Schottky diodes, thinking they would compensate for the missing 10 ohm resistor.
Which of these changes is keeping the circuit from working? I'm guessing it's the Sync/Mode pin but that's the hardest one to change.