Possibly, but also if the battery is in poor health that will be the way things are.
One thing to check, look under the bonnet at the earth, ie -VE post of the battery, there will be a "module/dongle" bolted to that post and is part of the -VE or earth lead, if you look closely, you should find a cable form plugged into that "module/dongle" - if that cable has been taken out or left out, that will stop auto Stop/Start "happening", so if it is unplugged, plug it back in and then press in to lock the small tab on the connector.
I'd be a bit annoyed if or when I buy a used car and someone has checked some of the
coding!