Are orcs immortal??

[Tuor Turambar,Cursed by the Valar]

If the orcs were, in a way, controlled by sauron or morgoth, then they would reproduce.

Elves don't reproduce in conditions of war or captivity. In Morgoth's Ring, when Elven marriage customs are being discussed, it is said that Elves do not have children during times of war, unsettlement, captivity, or hardship

MY THEORY
The quote about elven reproduction is true, but this fact is true because the elves have a sort of choice over whether to have children. It is not exactly a choice, but I thnk it would be POSSIBLE, although it would never happen, for elves to reproduce in a circumstance where, according to the quote, they would not.
Thus, Sauron could force the orcs to make this 'choice', so that they could reproduce endlessly.