I can't help but think if there are only 3 pairs, and each pair has 4 pups, the population is going to increase real fast.
That's why I feel the population is stable and not increase.
A certain percentage of the 3 pair's pups will not live to be adults either.
Jake, you say 3 pair so I'm using that, on your experience. The 3 pair know the 'holding capacity' of their territory. 12 new pups will not hurt chances of survival for the Alpha's. That show FOOD & Cover is available for 12 more Coyotes until dispersal.
Things can change and leave you scratching your head...
Now you have a lone Alpha male. He will look for another mate. This may take him from this area and may never return. The attending female may do the same.
Another Alpha females (one of the 3 pairs) may be shot or road killed. Pups will die. Alpha male may do same as the first.
Many variables. And pointing out some examples...'what happened? where are they?'
But the area does hold Coyotes now. And should continue to support Coyotes. Just pointing out there may be ups and downs in the populations from time to time.