florinc:
Isn't the "latching circuit" a microcontroller (running some firmware to read the button etc)?
Yes, the MC program has to be in the 'logic' loop if it's desirable to have a programmable auto-power off function, which is the whole point of having a solid-state power switch, otherwise a simple press on / press off manual power switch would be all that's required.
Here is the same concept that uses a latching relay rather then a FET 'power switch':
On pressing the manual momentary power switch, the MC starts and first outputs a digital high to 'set' the latching relay that 'seals' the power switch contacts. When the MC program wishes to power down it just outputs a low and the relay releases it's contact and the whole system powers off.
The advantage to using a latching relay with capacitance coupling (rather then a standard relay) is that once the relay is 'set' and the cap fully charged there is no continuous power being consumed by the relay coil, so this is as 'energy efficient' as the solid-state switch, about the same size and the relay can be had for $1 on e-bay.
Lefty