Welcome to the Forum! I have a new 2016 Crossback with Stop & Start and it took me a while to get used to it and to understand when it would and wouldn't stop the engine.
You don't say if you have a manual or auto gearbox as it behaves slightly differently for each i.e. you need to be in Neutral with the clutch released if manual, and have your foot on the brake or have the gear selector in N if an automatic.
There's quite a long list of situations where the start/stop won't work, and I've copied and pasted this from my manual:
STOP mode is not invoked when:
- the vehicle is on a steep slope (up or down),
- the driver's door is open,
- the driver's seat belt is not fastened,
- the vehicle has not exceeded 6 mph (10 km/h)
since the last engine start (using the key or the
"START/STOP" button),
- the electric parking brake is applied or being
applied,
- the engine is needed to maintain a comfortable
temperature in the passenger compartment,
- demisting is active,
-some special conditions (battery charge,
engine temperature, braking assistance,
ambient temperature...) where the engine is
needed to assure control of a system.
In this case, the "ECO" warning lamp
flashes for a few seconds, then goes
off.
By habit I used to apply the handbrake when stopped at traffic lights or in heavy traffic until I discovered that was the primary reason for my car engine not stopping as expected.
I hope this info helps!