Hello, I hope the following is of assistance.
The readings the dealer referred to are the state of charge of the battery, if the state of charge is below 72% then the start/stop feature is disabled to prevent any risk of a non start situation.
The battery is checked using a battery monitoring sensor (BMS) this works as follows.
The sensor measures temperature, voltage and current throughput of the battery. It uses this information to calculate the battery SoC (State of Charge) and SoH (State of Health). To function with high accuracy, the BMS must be recalibrated at regular intervals. A recalibration occurs during a rest period when the battery quiescent current is less than 100mA. This rest period must last for at least three hours. The longer the rest period, the greater the accuracy. The time frame in which a recalibration must take place is seven days. If the system has been unable to carry out a recalibration within seven days, the SOC accuracy cannot be guaranteed. This will result in the Start/Stop and SRC systems being deactivated. These systems will also be disabled if the sensor detects the battery is reaching its end of life, low state of charge or health.
Any charging of the battery needs to be done correctly otherwise the SOC and SOH will be calculated incorrectly and the start/stop will not work.
There are many other factors that will affect the start/stop function, engine temperature, air temperature, temperature inside the car to name a few.
To be honest 90% of start/stop faults I see are due to a battery fault it may be worth asking the dealer to check the battery and ask to see the start/stop battery test done if possible, this way you can see the results for yourself.
I hope this helps but if I can advise further let me know and I'll reply as soon as I'm able to.