Why does the dome light in a 2003 Honda CR-V burn out shortly after installation?

Not sure on your car but if it's got a halogen bulb and you touch it with fingers, it will burn out almost immediatly. On halogen bulbs of any kind you've got to use something n(gloves, paper towel, etc) to shield the bulb from skin contact during installation because any body oil from your skin will cause the bulb to overheat and burn out immediatly.