Not sure if its the same idea, but on a bmw I once had this would happen. I couldnt wire the lights up to the original light switch because some sort of electrical supply or computer would cut in and make it flicker. (not die completely)
I had to use a separate switch for the lights and they worked.
Guess you can try that? try making a switch to turn the lights on elsewhere and see if they both work together.
Pull the HID kit loom connectors apart.
Look at the pins inside the connectors.
Make sure the pins have not come adrift
and pushed through into the connectors.
This may be your problem.
One thing to keep in mind is the ballast's do need 13 odd amps at start up and I would think the existing loom (made for incandescent) simply can't supply enough. They are in fact very sensitive units and are very particular on the supplied voltage/amperage. Hence they attempt to fire but can't maintain as a pair but fire, warm-up and run as individuals.
You may need to upgrade the wiring. I'm also sure that if you attach your negative to the body of the car it would help. However I can't recall when Holden introduced negative switching (I think VX and up) so it shouldn't be an issue in this case.
I personally wouldn't keep attempting to utilise them until you rectify the supply as you will cook the ballast's.