I have an application wired per my crude schematic above with Schottky BAT42 diodes on each leg which has been running on 5v for many weeks and the lithium CR2032 backup battery is still showing 3.11vdc. So I don't see the need of the resistor in series with the schottky diode or two shottky diodes...doing this just drops the supply voltage to the DS1337 some more by the addition of the voltage drop across the resistor or the additional diode.
The DS1337 requires pull-up resistors between the I2C pins, the ALARM pins and the 5v source AHEAD of the schottky diode and NOT TO THE 3v SOURCE or the downstream connection to the Vcc of the DS1337. Otherwise a leakage path will exist from the DS1337 pins where the Pull-ups are connected to the MCU, and the MCU (which will sink current even when its 5V Vcc is shut off) will drain the backup battery. This recently happened to me and drained my backup battery in a few days while the 5v supply was shut off. I had to cut traces and re-wire the pull-ups to the correct location to eliminate the leakage path.
So I recomment to lemeur is to replace your standard diodes with low drop Schottky diodes (like the BAT42) and to double check how you have your pull-up resistors wired. That may be why your backup battery is draining so quickly.
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