Fine, if people simply don't believe Tolkien's words in the Silmabout Orksbreeding like the Children of Eru, perhaps the fact that they had to cross-breed with Men, and that their's onlyone way to do that!, to produce Uruk-hai!
I think it's more a case of them breeding when they're free from Ork-killing enemies. For instance, the population in the Misties increases by a lot between Bilbo's adventure and the War of the Ring, but this is because almost all had been wiped out first in the War against Dwarves, and then (more recently, so more relevantly) in the Battle of Five Armies. So basically the population was getting back to I guess it's natural peak.