Like @felmue I also did a bit more testing of the low voltage flags, then enabled the charge circuit (and setting the charge voltage via bfvsel to unlimited). The clock has held time ever since.
I'm curious about how long the capacitor can run the clock when fully charged and I have disabled charging again. But my device spends most of it's time on USB power so the duration is hard to measure; so lets try to estimate it :-)
If the frequency out and I2C is disabled (inien = True) the device should typically draw 0.3 µA when on backup battery (table 5 in the datasheet).
The capacitor is possibly a ML414H; 0.07 F.
Table 3 in the datasheet says that the clock oscillator minimum voltage is 1.1v, and the start voltage is VStandby; 3.3v. So we just need to work out the discharge time.
Start with working out the equivalent resistance at 3.3v; R=Voltage/Current = 3.3/0.0000003 = 11000000 = 11 MΩ
Now use an online discharge calculator to do the 'heavy lifting'...
https://3roam.com/capacitor-discharge-time-calculator/
(I like that site; it shows the maths used)
This gives an estimated! time of 845932 seconds; which is ~235 hours, almost ten days. Which seems reasonable for a capacitor backup.