Have a similar function on one of my cars, and with doing short journeys, it tends to drain the stop/start, but I use a CTEC charger on mine, once a month, charge it for 24 hours, and stop/start starts working again, so would suggest that you maybe invest in a ctec charger, best bit of kit I have purchased, as I also use it on my other cars and keeps batteries in tip top condition. got mine from a local company, but you can get them from a variety of places
https://www.tayna.co.uk/battery-chargers/ctek/mxs5-0/
Stu