So, let's do the arithmetic:
You say the lamp is 12V, 35 watts, so let's say it draws 3A nominal.
Battery is 7Ah, so theoretically, it should run the lamp for 7/3= 2.3 hours.
However: the lamp (the actual HID device) may be rated at 35 watts, but the converter isn't 100% efficient, so the actual current draw is probably more than 3A. Which might explain the shorter run time.
Do you have any way of measuring the converter's actual current draw? That would probably tell you something useful.
(Also, what condition is the battery in? Is it new?)