.... seems its got a mind of its own
Essentially that's hit the nail on the head.
As Colin says, there are lots of parameters the system takes into account before it will "allow" the stop/start to actually function. It's very diffcult to predict whether it will or won't. There are some things which will definitely prevent it working, A/C I think.
Personally I press the off button as a matter of course, but then I don't do heavy traffic so any stop/start benefit would be miniscule for me. It will work reliably if I take the car on a long run, but I don't do that very often these days (£2/litre approaching!!).
I have a 10yr old Yaris with an oldish "regular" lead/acid battery, nothing clever, and the stop/start will operate every time if I let it (again I switch it off as routine), Honda were extremely cautious with the programming of the Jazz mk.3 system.
Live with its foibles or switch it off.