With the clock demo, I notice the clock is only shown face up or face down, where even a weak battery, that no longer has the energy to lift the second hand up the face against gravity pulling it down, will still have enough energy to turn the hand.
If you want to use the Batterpoo in a clock, at least get a clock with "continuous movement" where the second hand is running at 8Hz, to give the illusion of a smooth sweep. Those clock mechanisms will on average use a battery every 2 months, while a regular clock will go up to 2 years with a standard AA cell.
I have one in my office, and, after the 4th battery in 3 months, I got tired of this continual change, plus it had a timekeeping that depended on state of charge of the battery, so it ran fast with a new cell, but ran slow as the cell went flat. Gained around a minute a day for the first 2 weeks, then fine for a week and then lost 2 minutes a day as the cell aged out, before going dead with a loss of an hour a day for the last 3 days or so. Took a feed from the cordless phone backup battery ( 12V SLA pack, 2 old alarm chargers, one for the battery, the second to give 5V5 to replace the DECT power brick output) and after a bit of trial and error on resistor values for the red led I settled on 6k8, a red led and a used 1500uF 6V3 non totally dead Crapxon (junk pile parts off an old PC power supply near to hand) across the LED as the voltage it gave the best results on. Now it runs on 1V35, and gives near perfect time keeping.
With the Batterpoo you will also need to look at time keeping accuracy, rather pointless to have a clock running with one when it will have a poor accuracy, only showing the right time every few months. At least a dead regular battery has an indication there is a fault, not a clock that runs, but loses time more and more as it goes on.