Mine also stopped working for an entire day, regardless of what I tried.....it was a cold winter day, most of the guys at worked also experienced the same issue....
The next morning it was back online...
How old is your battery? Are you doing lots of short trips?
Is the aircon/heat on, as the start/stop won't engage if the cabin has not reached the desired temperature, if this is the case then there could be a leak in your aircon....
I've read lots of posts stating that the start/stop won't engage until the car warmed up to operating temperature, this is absolute nonsense.....
Get the car on diagnostics to be safe
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