@rkauer:
The supercapacitor idea is potentially good, but unfortunately even with 470mF as you suggested, the backup time is less than two days.
Let's do the maths.
As I recall, RP5C01 draws around 15µA at 3.6V (when it operates in backup mode) and it stops working at around 2.2V. So with a supercapacitor's voltage falling from 3.6V to 2.2V, that's around 61%, so close enough to one capacitor time constant (63.7%).
To work out the equivalent resistance of the RP5C01, where R=V/I, then 3.6V/15µA = 240k ohms
And as we all know that T(seconds) = C x R, then the capacitor discharge time to one time constant is 0.47 x 240k = 112800 seconds, or 31.3 hours.
Supercapacitors are far more suited to modern RTC devices and memory backup applications where only a few nA are drawn from the capacitor.
When replacing RTC batteries, I generally use the original Varta Ni-MH battery which have a rated lifetime of around 6 years. I put a printed label inside and outside of customer's machines stating when the battery was replaced and whan it should be replaced by.
More details in some of the guides I've written
here if anyone wants to know more.