My bulb when out last year, and I was told to TRY this by the guy at the lighting store when I went to buy replacements...

Unplug the light so NO power is going to the fixture. Remove the bulb(s) - use a dry rough cloth and clean off the end post thingies (I don't know what they call them)and check where the bulbs connect - if you can, clean that part as well (a small dry brush or something tiny to brush off in there).

I was told that sometimes just a little spec of dirt/dust can prevent a good connection for the bulb.

Put the bulbs back in, making sure they "lock" in tight.

I did it - it worked - and a year later that bulb still lights when I need it.

Doesn't hurt to try ??