PROBLEM
Passenger side low beam light goes off frequently,
although it comes back on when the switch is turned off then back on.

ATTEMPTED RESOLUTION #1
Tried to replace the HID ballast, but after disassembling the bumper and headlight,
the aftermarket ballast wouldn't fit and had to return it. Can't seem to find a reliable
aftermarket ballast with good reviews. Trying to locate a used OEM one instead.

ATTEMPTED RESOLUTION #2
I noticed that passenger side HID bulb doesn't look all that great.
The center (white) part seems to be leaking or bubbled up
when comparing it to a new one.

I paid ~$60 for one bulb to get an identical Phillips D4S HID bulb when
cheap aftermarkets ones sell 2 pack for as low as $20, in hopes of getting a longer life.

RESULT
The new headlight now stayed on entire 30 minutes of test driving.
The old headlight used to go out within 5 to 10 minutes.

All seemed good, except, now I hear a faint but clearly noticeable buzzing sound
when the low beam headlight is turned on. When you start the engine, engine noise
is loud enough to wash out this buzzing sound.

Then, I read on many blogs where HID users are complaining of buzzing sound.
So I carefully listened to the (good) driver side light, and sure enough I hear the
buzzing sound here as well...although it's much more faint and quieter than the passenger side.

QUESTION
Does your HID headlight make a faint but audible buzzing sound when it's turned on?
Is one side louder than the other?

Does anyone's HID headlight doesn't make ANY buzzing sound?
You have to really get close to the headlight to hear the buzzing.

Here is the OLD and NEW HID bulb pictures.
Noticed that in the old bulb, the center white area (I believe it's sort of chemical that produces different color light),
is all puffed up.

 

Yes, my car does it too. I can hear it at 2.5 meters in front of the car. My ballasts are OEM and new from last September, but it has never worried me and I never had any issues with the headlights because in fact, I've heard that kind of noise from pretty much every car equipped with HID headlights. In more recent cars, the way the front end is designed may make them silent, but if you open the hood and listen closely, you will probably hear it.

By looking at your bulb, that was clearly the culprit. When they are burned out inside, they are done. You were right buying a Philips, these will last a very long time.

 

Subscribe what PauloFR is saying. When they turn on, I hear the buzzing sound. I do believe it is a normal sound. I don't need to be in front of the car to hear. If parked in narrow garage, because of the echo I easily hear them inside the car (with open window).

Although I decided to go with the 20$ white, cheap and so what reliable bulbs. Reviews are good so what the hell. But I believe that Philips bulbs could be sharper in terms of the light. Good quality requires good investment.