Dimmer circuit - some bulbs not working

Hi

So I have a (twin) dimmer circuit with 4 spotlights (Par 38 80W screw type). Some time ago, one of the bulbs stopped lighting. I don't use the room that much, so I just resolved to buy a bulb next time I was in the shop. I duly did that and went to replace the bulb, but the light still wouldn't come on. Each dimmer switch controls two bulbs, and the other one in that part of the circuit worked fine.

I assumed that I must have a loose connection in that light socket or something, so I decided to try the original bulb in a different socket, where it duly worked. So the bulb isn't blown. I had a look at the socket in the ceiling and couldn't find anything obvious in the way of loose connections. At that point I just put back in the bulb and resolved to come back to it later when I had found out what the problem might be. I'm ashamed to say I left it that way for the last year :rolleyes: As I said, I don't use the room that much and 3/4 lights were working.

Now another socket has stopped working - I now have one working and one non-working light on each dimmer switch
So I've decided it is time to do something about it. Any suggestions as to where I should begin?