Here is some information about the storage & keeping of blue crabs from the Blue Crab web site http://www.blue-crab.org/buying_hards.htm
Hard blue crabs are always marketed live. Crabs that have perished in transit should be immediately discarded since there is no reliable way to determine the degree of spoilage. Motion and heat are the biggest factors affecting the blue crabs mortality.
The best way to store a hard-shell crab is in a cool, moist environment. It is important to store live crabs at a 50-degree temperature. Holding live crab in a standard refrigerator (36-degrees) will ultimately kill the product. While producers suggest that the shelf life for hard-shell crabs is 2 - 3 days that includes all of the shipping and processing time.
Crabs use their gills to take oxygen out of the water, much like a fish. However, crabs can survive for long periods out of water. As long as a crab can keep its gills moist, oxygen from the air will diffuse into the moisture, and then into the gills. To keep a crabs gills from drying out, store them in a cool, moist environment. Crabs have articulating plates around their gills that help seal them in and prevent drying out.
When you buy (or catch) live crabs, you should place them in a suitable container. A cooler with a layer of ice on the bottom is best. Optimal temperature is 50-degrees. Fasten a shelf to keep the crabs out of any melted ice water. If the crabs get into this water they'll quickly deplete the water's oxygen and will suffocate (for this same reason you should not keep live crabs in a bucket of water). Be sure to keep the lid cracked so that fresh air can get in. Alternatively, you can store the crabs in a wooden bushel basket, covered with a damp burlap sack, and out of direct sunlight"