You didn't say whether these halogen lights are 12V or 240V in your last post, but I suspect the former.
In which case the small box you refer to inside the rose is a driver, and you are overloading the driver, which has some kind of thermal reset when this happens.
There will be one driver for each light, if the 12 lights are spaced all over the ceiling.
If, however, you have a single bar with all the halogens driven from one ceiling rose, then there is one single driver (of about 120VA) inside the rose, and you are still overloading it by what you have done.
You need a driver of at least 240VA. That (if it exists) is going to be quite a size to stuff up inside the ceiling cavity and cost around £45. At a quick search, I couldn't find one bigger than 210VA - which would only run 10 off 20W bulbs.