Under cabinet puck lights that continually burnt out

If you touch them with your fingers or contaminated, they will burn out, a dimmer could extend the life and have a good effect.

Are they regular Halogen? Low voltage Halogen?

What model # are the fixtures? I'd bet you have 20w halogen or 18w xenon lamps. Both lamps run very hot which shortens the life, especailly in an enclosed UC fixture. How are the lamps attached? Do they have 2 pins, or are hey a wedge base? See if the pins on the lamp are black or burnt. The brand makes a big difference. If you are thinking about replacing them, LED's have come way down in price and might be worth considering.