I own a 2015 XF petrol car, and after much research on the stop/start system, I can offer a suggestion.
In the XF for example, there are two batteries. A large AGM type, that is used for starting the vehicle, and a smaller battery that runs the auxiliaries such as radio, lights etc, but also the stop/start function of the car. If this battery goes flat or dies, so does the stop/start system. In my case. being 7 years old, it had died of old age, while the AGM was still going strong. Replacing both fixed the problem.
While on this subject, I, like many others, and knowing how older starter motors functioned, was convinced that the motor pinion and ring gear would destroy each other with so many starts.
However this is not the case. The new starter motors used in stop/start, employ two activation solenoids, known as Tandem solenoids. When the car is almost stopped, the first solenoid synchronises and engages the starter motor pinion, to mesh with the ring gear, and stay meshed. When the foot is lifted off the brake, the second solenoid energises the starter motor, which being already connected to the ring gear, start in a fraction of a second.
Of course both the main battery and starter motor have been uprated.
