Daystrom Institute

There's a couple things here. The most obvious explanation is that there just weren't very many Constitution class ships in service, and their attrition rate was brutal.

As for why there were so few in the first place, and why more were not built to replace the losses, the conventional wisdom prior to Discovery coming out (and perhaps it still holds) was that the Connie was actually substantially less automated, and less well designed to facilitate automation, than it's rough contemporaries and immediate successors. The Connie refit gives some support to this assertion in that an extremely extensive rebuild was apparently necessary to get the ship to modern standards only 20ish years after their original commissioning. Such an extensive refit process could very well have still fallen short of what a brand new ship designed from the ground up to use the latest tech was capable of, meaning that it was more cost effective to crank out Excelsiors where frontline ships were needed, and far more cost effective to build Mirandas and Oberths to do lightweight tasks in safe areas.

In other words, the Constitution class was an awkward, inflexible, and inefficient design which happened to be in the right place, at the right time, and just good enough to have a staring role in a key period of Federation history. It carved it's niche and made it's mark, but was rightly supplanted by better ships as Federation technological and industrial capacity progressed into the late 23rd century.