You need to check the voltage at battery terminals

You need to check the voltage at battery terminals when the engine is running. If it is 14.2 volts, then the battery is getting charged. If the voltage is less than 12, the battery is not getting charged. I am suspecious that the battery is not charged. That is why it is draind after a while. You need to check the connection between battery and alternator to make sure connectivity is there.