That's what happens when you fit cheap HIDs.
I hope youve got projectors fitted, if not I won't he giving anymore advice after this.
When I had my fiesta, cheap 35w hid kits wouldn't work properly. I fitted a fairly decent 55w kit and for whatever reason that just worked. I didn't even have to install a Relay to the battery. In your case, it could be a case of either the ballast being faulty, or, it's not able to draw enough power to keep the bulb lit.