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I think you should never disconnect the battery while the car is running. Depending on its design, the voltage regulator circuitry will probably sense that there is no charging current available for the battery and will attempt to raise the alternator output voltage, possibly to an extreme value. This can damage many things, including a replacement alternator, engine controls, etc.
Previous posts on this site show how to harmlessly check the charging system for proper voltage with a meter. As stated in other replies you got, you can use a meter to check for current drains with the car not running. This would include things like the glovebox light, corroded or salt-damaged wiring, etc.
Are you sure there is not an internal short or other defect in the battery itself?
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