In my propeller clock that I designed some years ago, I used Philips 8563 RTC that is known for its very low power consumption. I used neither diodes nor resistors and connected pin 8 of the RTC directly to + terminal of 2032 Lithium battery. The 4.7K pull-up resistors of the RTC are connected to 5V. Since 2032 battery is not meant to be charged, there is no need to connect it to 5V rail. The only device that the Li battery is powering up is the RTC. So, how long the battery lasts is purely dependent on the power consumption of the RTC and the shelf life of the Li battery. In my circuit, even after 4 years, the RTC is working fine.

I am sure, DS1337 is very similar to Philips 8563 and you can try connecting the battery to the RTC without the diodes and resistors.

Bala