The Stop/Start system on these is at best dimwitted and cheap.
What everyone is telling you is true, it will only work with the battery in A1 condition, with little load on the electrical and HVAC systems and the engine at operating temp.
Unfortunately the system isn't really suitable to keep the battery in A1 condition, is self defeating.
It's nothing more than a switch/sensor attached to the normal starting system with just a heavier duty battery and cables.
Energy used from the battery has to be replaced, to do this the alternator has to work harder and use more fuel.
So every time the engine stops and restarts, the engine uses more fuel to work the alternator to recharge the battery, though this takes time.
Normal batteries don't really like being worked like this, so in most cases (but not this one) more advanced batteries (AGM) are used to cope with this.
So you end up with a battery that's good enough to start the car on the key, but the sensor on the battery won't let it self stop as it detects the battery isn't quite up to a restart, so the alternator is constantly working to try and recharge it to the required level.
The fix, you'd think would be to perhaps fit a bigger, stronger battery, but this would now cause the alternator more problems as it would have to work even harder to try and recharge the thing.
So what about fitting a more powerful alternator to charge the bigger battery? That will require more fuel to turn the feckin' thing!
Like I wrote, the system Fiat use is self defeating, it's just a fudge to report lower emissions. You'd probably be better off switching it off altogether.
Better systems utilise wasted energy or use other, free means to perform the restart, these tend to work better and actually save more fuel as you are not having to recharge the battery after the restart.
Mazda's Styactiv system stops the engine with a cylinder on the compression stroke, then fires that plug to perform a restart.
Other systems use energy captured from engine braking via a hybrid alternator, this is stored in capacitors which is then used to turn the alternator to bump the engine back to life rather than the starter motor, as it's a quicker restart and more efficient and doesn't detract from the main battery.
I've a diesel Citroen e-HDi with the later system and it works every time once the engine is warmed up. It actually switches the engine off before it's at a standstill (under 8mph for the auto/13mph for the manual), so you coast the last few yards saving even more.
It restarts in 400 milli seconds very smoothly and it actually saves fuel.
I've worked out my trip to work and back is around 8% more efficient with it on than off.
My Panda didn't make a difference as it never knocked off!
My Abarth hasn't a stop start system, then again with a Monza exhaust on it, why would you want is sitting there silent at the lights?