Aftermarket HID conversion

I just installed a new HID conversion kit for my car. Install was easy and triple-checked, and upon start-up, both turn on but after a few seconds the passenger side headlight flickers off. However, what seems to be confusing me is that if I turn on the car's lights, but keep the engine off, both lights illuminate and stay lit. If I keep them on for a few minutes and then turn the engine on, my lights have no problems. It seems to me as if the lights need time to warm up before the engine can be started. But why is this? I've done some research and haven't really come up with anything. Please help!!

-Kevin