AlxDroidDev:
Considering the minimum voltage required by the DS1337 is 2.5V, a 0.7V drop caused by the diode would bring a brand new CR2032 (3.2V) to the minimum required supplyby the IC. I am afraid that whenever the battery gets to 3.1 or 3.0V, it would no longer be able to power the DS1337 in offline mode.
I can understand your concern. In my case this isn't an issue as the datasheet for the PCF8563 claims that the clock will continue to operate all the way down to 1v.