Problem with spotlights in my kitchen - how do i fix a loose connection?

I have 9 spotlights in my kitchen and the other day when i switched them on 6 of them went out. At first i thought the bulbs had blown but they have flicked on and off a couple of times since so i think it's a loose connection somewhere. Does anyone know how to fix this or do i need an electrician. I've taken the bulbs out but can't seem to get the actual fittings out of the ceiling to have a look myself - can anyone offer any advice? Thanks!