By the time of the Flavians there were large reductions in the supply of slaves, both those peacefully imported from outside the Empire and those captured in military campaigns. It was a time of decline for every large latifundia farm-households and, a little bit later, during the Antonins' rule, slaves became purely luxury items, not a source of profit. So, I'm interested: if the Romans noticed the shortages in slave supply, why didn't they set up some sort of breeding centers for slaves in order to maintain their population?
One reason was a gender imbalance, a lot more male slaves (captured in war), than female slaves.And of course, "breeding" requires both.
When slaves were shipped to from Africa to America, there was a reasonable balance of male and female slaves that were bought or captured, and taken across the Atlantic in ships.
Very few ancient ships carried large numbers of women.The carvels of the Middle Ages were sufficiently comfortable to accommodate women (some came over on the Mayflower, for instance).