To be sure, we don't have direct evidence of any ships being built during the war. The only "new" ship to emerge would have been the Sao Paulo, but she might also have been in existence and service/mothballs since before the war, even though the implication is that she's fresh off the docks.
It might be that it takes several years to build any reasonably sized combat starship. Which would probably mean that Starfleet would gain significantly in ships - but at the very end of the war, rather than during it. Whether that gain would balance the losses is unknown.
I disagree here. There is a lot of talk of ship building during the lull in the Dominion War, though the classes under construction may be of some debate. I find the idea that the Federation, an organisation of massive resources, with its economy tilted definitely towards war, would take 3-4 years to build desperately needed ships, a bit odd.
Many ships were built is the impression I get, as well as the hundreds taken from mothballs of Miranda and Excelsior design, Starfleet might have needed hundreds of Akiras, Steamrunners, Intrepids and Defiants.