Sometimes it is the power supply, but I've also had a number that died simply because one LED burned out and failed open. Because they are wired in series it only takes one failed LED to take out the entire bulb. If you're a cheapskate you can sometimes get a bulb working again by testing the circuit and bypassing the burned out LED with a jumper wire.

If the bulb dies but you notice that all of the elements are still just barely on (like a dim spot of light in the middle of each one) then that's a good indication that you have a dead LED.