What's the problem with our 12V halogen lighting?

We have 6 12V halogen lights in our bathroom, controlled by a dimmer switch. Each light has a separate transformer. Two bulbs have recently gone out, and the lights still don't work with replacement bulbs. I've had a look at the transformers, and can't see any kind of reset switch. They were installed about 12 years ago. Any suggestions, or have the transformers simply failed and need to be replaced?