I've had the 5F supercap in TZ for just over a week and here are the results.
With D2 replaced by a 100 ohm resistor, it takes about an hour to charge the capacitor as expected.
After a week of the game being off, the capacitor voltage is around 2V. The memory settings are still holding, but the timekeeping is way off.
There are 2 separate things going on here:
1) The capacitor is self discharging due to inherent parasitic leakage. The manufacturer of the capacitor lists this as 25uA on the datasheet. A bit of RC calcs shows that with this leakage, the capacitor will discharge on it's own in about 23 days.
2) Current is being consumed to a) Support the RAM and b) Run the real time clock/calendar. This measures out to a total of 20uA. Adding this to the 25uA for leakage gives 45uA. More RC calcs shows that with this total current, the capacitor will discharge on it's own in about 14 days.
However, the 2 loads a) RAM and b) real time clock/calendar each have different minimum voltages to "stay alive". The real time clock/calendar seems to stop working at about 3 volts while the RAM seems to hold it's settings all the way down to near 1 volt.
The result is that after about 3 days, the real time clock/calendar will start to lose time. After about 10 days, the RAM settings will be lost.
The RAM current can be reduced by installing Non-Volatile RAM (NVRAM), but if you want accurate timekeeping, the capacitor leakage will still do you in after 2 weeks.
One key point is that bigger capacitors offer no help. The leakage of most supercaps is essentially proportional to the capacitor rating. Larger capacitors or multiple capacitors in parallel yield no help.