What bulbs do you have in the lamps.
Have you tried the working one in the problem socket.
Is there anything else connected to the dual socket.
Have you tried the CM15 plugged into one of the problem dual sockets and the AMG in the other one.
Also try swapping the lamps around.
Check the wiring connections in the sockets sometimes if its loose this can cause problems.
Have you recently bought anything that you may have plugged in.
Are you in the UK or elsewhere in Europe.
Are you sure its called an AMG2 or is it an AM12G.
Lastly try switching circuits off at the consumer unit. Does this improve the situation.