I have an earlier model of the nanoKenbak-1 and the RTC battery was depleted, it differs from those in the current versions.
After desoldering it, I noticed that I actually liked how the nanoKenbak sat flat on the table without the battery in place. That got me thinking—it might be worth relocating the battery entirely.
Eventually, I tried an idea to eliminate the need to replace the battery. I connected the clock chip (a DS3231) to the lithium battery using a Schottky diode and a capacitor.
I then began testing the setup by removing and reinserting the Lithium-ion Coin battery (LIR2032) to see whether the capacitor could maintain the time during those short gaps.
I found that if I replaced the battery in under 15 seconds, the clock continued to keep time without issue. If I keep the battery removed for a few minutes, the clock stops but the time is not cleared.
I recorded the lithium battery's voltage decay over 40 days of powering the RTC. The battery lost 70 mV, and the time remained accurate.
Today, after a month and a half in the box, I checked the time and it is still correct.
I'm adding a picture of my modification and another one showing what it would look like on the current nanoKenbak-1.
NOTE: This may be a way to void any warranty the product has. :)