Why does my Android Tablet battery uncharge when it is off and not in use?

It is, but only if it is in sleep mode. If it is powered down then there is a problem. Look for any active widgets or mail checking/syncing issues. Try a restart if you haven't already. There are a few tools that will tell you what is using the battery like gSam Battery Monitor.
 
Any time you're not using the tablet radios (WiFI, Bluetooth, GPS), turn them off. As pointed out by leeshor, they'll use power even when the tablet is "sleeping".
 
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