Maple trees are able to tolerate soggy soils, so it's not surprising that the one maple tree thrives in the soggy site although grass doesn't. It may be a combination of shade from the maple and wet soil that prevents the grass from growing in that part of the yard. You have a couple of options. Depending on the lay of your yard, you may be able to bring in some fill and raise the soggy section so that it's no longer wet all the time. Another possibility is to grow something other than grass in the wet section. There are shade- and moisture- tolerant plants that should do well here. If you want a grasslike look, sedges would be a good choice. Many of them grow only 6-12 inches tall and have grassy foliage that may be green, gold, or variegated with stripes. Hostas would also like the shady, moist conditions that you describe.