Storing a battery on a concrete floor will *NOT* discharge it. All lead-acid batteries will naturally self-discharge which can result in loss of capacity from sulfation. The rate of self-discharge is most influenced by the temperature of the battery's electrolyte and the chemistry of the plates.
In the early 1900s, when battery cases were made of porous materials such as tar-lined wood boxes, storing batteries on concrete floor would accelerate their natural self-discharge. Modern battery cases are made of polypropylene or hard rubber. These cases are sealed better, so external leakage-causing discharge is no longer a problem, provided the top of the battery is clean and free from wet or dried electrolyte.
Having said that......large differences in temperature could cause electrolyte stratification within very large batteries (>250 AH) which could accelerate it's internal "leakage" or self-discharge if the battery is sitting on an extremely cold concrete, stone or steel floor in a warm room, boat or submarine. Stirrers or bubblers are often used on these types of large batteries to keep the electrolyte from stratifying.
Here in my lab, I have a 40,000 Amp capacity battery, sitting directly on the concrete floor. It's worth a shitload of money and is critical test equipment to my company....so we wouldn't do anything to screw it up!
For maintennence you could get something like
http://www.dse.co.nz/cgi-bin/dse.sto...uct/View/M9531
at $35 - odd, it's cheaper than a new battery!
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