Why does my new 220V AC to 12V DC transformer only allow one Halogen light to work?
You are overloading your current supply, it is shutting down to prevent damage.

2 x 10W = 20W

Which is more than 15W.

It seems the only options are buying 5 of this "converters" (one for each lamp) or buying another model which can handle more power (more lamps per converter).