Death Angel-
I didn't realize the power supply was fixed - no controls. I don't know your level of knowledge of electronics, and I certainly don't want to insult you in any way!
But, are you sure the LM317 circuit is wired correctly? How are you measuring the current to the diode? Ideally, you should place a .1 ohm / 1% resistor in series with the diode and measure the voltage across it (if you don't have one, I can send you one) - ohm's law dictates that the voltage in mV x 10 = mA current flow. Most digital multimeters are unreliable in current measurement except in the 10 or 20 amp mode where the shunt resistor is very low, but the accuracy is still questionable. I've burned up a few diodes, instantly, usually by shorting the power supply leads accidentally - when they "un-short", poof.
As someone mentioned before, you should place the cap (27 - 33uF) on the diode leads, also to be really safe put a 1N4001 across the diode in reverse. Sorry to hear about your 3 in a row - but there has to be a reason.
Rob