Li-Ion Rechargeable 2032 Button 3.6V Cell and Arduino
Application of 5V directly on a Li-ion battery will overcharge and damage the battery at least, and at most will cause overheating or fire.  You will want to charge a 3.6 volt battery with a constant current until it reaches 4.2 volts, then hold the voltage here.
Your low loss diode is likely not what is draining your battery.  Cells of this size are designed to provide currents under 1 milliamp for hundreds of hours, but they don't like high currents; at tens of milliamps, you will see the voltage drop in seconds, although the battery may recover if the voltage is removed.  If your load is down in the milliamp range and your battery is still draining quickly, it is likely damaged.