bad H.I.D. problems... any ideas?

Is there a relay in this kit? Did you install it? Is this a both high and low beams kit? If it is just a single beam then I stand by my previous answer...pins in the plug in the wrong configuration.

You likely have a relay if this kit is both high and low beam, but you would likely not have a relay if it is just a single beam.

Here is a picture of a relay (geez, just use Google images to search for "HID relay") The square box type thing in the foreground is the actual relay.

Was this issue ever resolved?

I think for us to help, you need to post a link to the installation and wiring instructions for your HID kit.
If yours uses a single bulb design with a mechanical shutter for hi/lo beam, then a relay is often used to power the bulb. The relay coil is connected to both the factory hi-beam and lo-beam wires with diodes so the relay remains activated when you operate the hi/lo beam switch. If your kit is wired this way, but only the lo-beam setting has problems, it could be caused by worn headlight switch contacts.

However, if the wiring is done some aother way, or there are 2 separate bulbs for hi and lo beams, there could be numerous other causes.

ive had probems with hid relays on 2 sets of hids, one ebay and one vvme.com. make sure the relay doesnt get wet because it will start corroding and shorting out. i bet that is what has happened to yours. you may not want it but my advice is to buy a new set of hids. and get them from ddmtuning.com They are cheap and awesome quality. thats what i have in my stang, my truck and my gf's stangs. full digital ballasts and lifetime guarantee. you cant beat it.

Several ppl have mentioned the alternator angle. It does not appear to me that the OP has correctly ruled it out.

Consider this theory. The HID's are kicking on with an initial "surge" of power. Remember the HID’s do have a ballast. This is over whelming the alternator and collapsing the field coil. The alternator shuts down. This causes the HID’s to shut down. This removes the "load" from the alternator. After a small delay, the battery re-charges the alternator’s field coil and the alternator begins to output voltage.

The cycle repeats.

To everyone. A strong battery is required to maintain the reserve power for the alternator’s field coil. A weak or dead battery means weak or no alternator. Don't think that because the car is running that a bad battery can't be at fault.

To the OP, double check the battery terminals. Are they clean and tight? It amazes me how frequently ppl will replace a battery but think nothing of the corrosion cauliflowers growing on the battery terminals. Corroded battery terminals can render a new battery useless.

Have the alternator tested and confirmed for proper output as well as tested for excessive AC ripple. Most autoparts stores will do this for free. While there, have the battery tested as well.

Measure the voltage across the battery terminals while this is happening. What is it doing? Is the voltage constant or is it varying wildly as the HID’s fire up and shut down?

In looking at the video posted in the OP, the problem is not in the ballasts or the power being delivered to them because the fogs are blinking in time with the HIDs. This suggests power to the lighting circuit is being interrupted upstream of the ballasts and bulbs.

I don't believe for a second that a battery that can supply hundreds of amps to turn a starter motor is so overwhelmed by HID ballasts that the alternator field goes down.

This brings back fond memories of ca. 1975. My old man had a 1974 Mercury Marquis (land barge) and decided one day to upgrade the headlights from standard incandescent to then-new halogens. After installing the halgoen sealed beams we were met with flashing headlights, much like the video (though in the Merc's case, the flashing was more regular.) That car had a circuit breaker in the headlamp circuit that was tripping because of the extra current drawn by the halogens. Looking back, it was actually a pretty cool thing to use a C/B instead of a fuse.

Having said that, HIDs actually draw less current than standard bulbs after the initial power-on so it'd be surprising if the OE circuit has a problem with power but you never know...

If someone has a complete schematic of the Mustang's headlamp circuit, including all relays, fuse links, circuit breakers and the like, post it so we can analyze it. It's likely to turn out that the

headlight wiring diagram 85-1

Trinty_gt, you do have some good points. If it's ok, can I expand?

Consider that the Mustang DOES have a automatic reset circuit breaker in the head light switch. It is a nothing fancy thermal CB that trips when it gets hot. And resets when it cools down.

I do not believe it is a CB because if it were, ONLY the head lights would be affected. Secondarly, I don't think it is possible for the CB the heat up, trip, cool down, and then reset so quickly. The period of the event is just too fast.

The single point of electrical failure for the fog lights and head lights are the head light switch itself and the car's base charging system. There is a fog light relay that could be dropping out if the voltage is dropping to low. But if so, this points straight back to "sagging" voltage and the car's base charging system.

While it is true that HID's do use less current when working, the problem is the HUGE initial inrush of current needed to start the ballast. The point about a battery being able to supply hundreds of amps is valid. However, what is not known is if corrosion is limiting the available amps. Perhaps this also offers an explanation of how it worked for a while and then started failing.

Another possible cause could be something as simple as corrosion at the small wiring connector at the alternator itself. That is were the power for the alternator's regulator comes from.

In anycase, this issue can be easily answered by a simple voltage test at the battery while the problem is happening. With the shortage of real tests by the OP, the fact of the matter is it could be a great number of things. And all of this is just an "educated guess".

Head light and fog light wiring diagram 85-1 attached for review.