A lot of people say the carbs on the Bandit 400 are hard to clean. I don't think thats really the case, it's not like they are some sort of fancy special carburator. They are just small, thats all, and prone to gumming up because of this. You just have to be thorough. That being said, a lot of shops don't want to touch the 400 because it is a 10+ year old bike with parts that are -really- hard to get at times.
Something else that can cause the symptoms your describing, Badidou, is either a failed voltage regulator or the Igniter going bad. The igniter is a pain, the regulator not so much...
There is a FAQ on this forum somewhere about repairing your own igniter, though, so if this turns out to be the problem you may want to try that route.