HID Lamp Ballast Using TI UCC2305
There will be a tolerance on the breakdown threshold of the lamp and the ballast must meet or exceed the requirements of all bulbs.

The typical xenon headlamp operational values may not match this bulb exactly;

1) Turn-on stage (T1 ≈ 30 ms) V>=360 V
2) Ignition stage (T2 ≈ 100 ns) 23~30 kV
3) Take-over stage (T3 ≈ 300 μs) 10~30 ohms with 12 A peak decaying in xxx μs
4) Warm-up stage (T4 ≈ 20 ms) voltage is temperature dependent 2.6 A
5) Run-up stage (T5 ≈ 6~10 s) cold lamp comes up from  20~30 V to nominal 85 V
6) Steady state (T6) 85 ±17V, 35W max., 250~400 Hz
Ref

Failure at any stage is due to the electronic ballast tolerances meeting the bulb specifications.

The obvious question is which stage # fails?  2, 3, 4 or 5?
Show the output Voutsense, Isensein, Iloadsense during start-up.
Compare lamps.