There's a couple of nice quotes from text 10 of the "History of Middle Earth" (Morgoth's Ring) that directly address the issue of orc immortality and orc lifespans:
"They needed food and drink, and rest, though many were by training as tough as Dwarves in enduring hardship. They could be slain, and they were subject to disease; but apart from these ills they died and were not immortal, even according to the manner of the Quendi; indeed they appear to have been by nature short-lived compared with the span of Men of higher race, such as the Edain"
Robert Foster's "Complete Guide to Middle Earth" notes that the average Edain lifespan is between 70-90 years, which suggests that average Orc longevity (barring illness and injury) is somewhere around 60 years of age.
It seems that the fact that certain (immortal) maiar were posing as Orcs gave rise to the myth that the orc race was immortal...
This last point was not well understood in the Elder Days. For Morgoth had many servants, the oldest and most potent of whom were immortal, belonging indeed in their beginning to the Maiar; and these evil spirits like their Master could take on visible forms. Those whose business it was to direct the Orcs often took Orkish shapes, though they were greater and more terrible. Thus it was that the histories speak of Great Orcs or Orc-captains who were not slain, and who reappeared in battle through years far longer than the span of the lives of Men.