I do a lot of pre-sale and rental maintenance and thought that I might share what I have found with low voltage downlights, I have found them to be a high maintenance item second only to dripping taps.
When you pull the old globe have a look at the contact pins they should both be bright and shiny, if either is a dark colour then you may have a socket with a faulty/poor connection, I believe that the bad connection causes localised heating between the socket and contact pin, the heat gives rise to oxidisation of the pin causing the dark/black colour and eventually a failed contact.(The sockets carry about 4 amps and it doesn't take much of a bad connection to cause localised heating. Compare this to a 240v 60w lamp which only draws about 0.25 amps). A bad contact would explain the 'going on and off at will'
A new globe may be a temporary fix until that too goes the same way as the previous globe. In this case you need to replace the socket as well as the globe, if the socket is one of those with grub screws that hold the globe then replace it regardless they are a major cause of trouble. You don't need a sparky to replace the socket as only a low voltage circuit is involved.
You can buy the 12v sockets at bunnies or most larger hardware stores. My local bunnies sells a non dimable downlight set consisting of ceiling fitting, globe, socket and switchmode transformer for about $8.00 or so.
Also a trap for those that may have a problem and want to measure for the presence of 12v at the socket. Many switch mode transformers (these are smaller and much lighter than the older magnetic type) will NOT startup without a load which in this case is the globe. If you try to test for the presence of 12v and there is not a working globe attached the voltage will measure 0v even if the transformer is good.
I have also come across a NZ made transformer labelled 'de-lights' with an integral fuse on the 12v side of the transformer, I've found bad contacts in the fuse holder and also broken connections.
