What limits a starship that can manufacture another ship?

Could an advanced starship use its onboard machine shops to build more ships?

Potentially yes, but the ability to manufacture hulls does not solve the shortage of trained crews needed to operate them.

Given enough time and resources, a Glorious Heritage-class cruiser could rebuild and rearm itself. That capability suggests it could also construct another ship away from a conventional yard. In this proposed explanation, Dylan Hunt's shortage of crews is the reason to avoid stopping and building more cruisers. Manufacturing another hull would leave the separate problem of finding people to operate it.