Scott,
What Donnie said generally applies. I also wonder if you had done any topdressing with it before the coring program? Did your topdressing go pure sand, or did it have some brew of organics in it?
Sometimes, a layer develops at the interface of old and new sand, just an inch or two below the surface, holding water too near the surface. IF the sand is as fine as you describe, I suppose its also possible the water is coming back up in part due to wicking action, although the layer holding water would be the most common problem of squishy greens.
The coring should help ,if this is the problem, gradually cutting through the layer, but as Donnie says, equal sand to original construction is best, coaser sand next best, and fine sand often a recipe for disaster.