GU10 Replacement?

Hi
Our house is fitted with ceiling downlighters - several in each room - all about 7 years old now.
Occasionally, one stops working and I undo the clips, disconnect from the fitting, replace - and hey presto - it works.
However, in the downstairs bedroom - in which there are 2 downlighters, the replacement doesn't work.
The bulbs appear to be all GU 5.3 MR16 50W 12V.
The bulb that works in one downlighter fitting doesn't work in the downlighter that stopped either.
A couple of years back, this happened in our sitting area - which has about 8 downlighters. My daughter's boyfriend knew what the problem was and fixed it in a minute.
Any idea what the problem might be?
Many thanks