No mine it didn't do it straight after fitting the kit.
Hid's don't use anymore power but need a constant stable supply to the ballast. When your cranking the power is dropping so the light goes out, it was probably happening before with the halogens but they would have just dimmed instead of going out.
I'm pretty sure it's your battery.
Check the voltage with a multimeter when cranking with the lights on or connect some jump leads up to another car and see if it still dose it