It's an entire species. The idea that they only had kids the once and then they sent them all away is just obtuse. No sentient race could survive with a reproductive strategy like that.
The Founder were at one time solids, during this time period it would be easy to see them have offspring in the "normal " way, but this is not a given.
Once they change from solid to goo, why would regular child production be necessary? We've seen extremely short lived races, and other that live basically forever. If the Founder don't normally age and die, then the replacement purpose for children disappears. Founders can be killed, and the hundred were once produced for a specific purpose. There might be a need for periodic replacements. But these occasions might be thousands of years apart.
Akuta: "Replacements. None are necessary."
What is relevant is that there has to be a mechanism to counter them in case they do.
Ahhh, the lovely smell of paranoia.