I had the battery flag for the stop/start not working on my car when I got it. It was only 2 yrs old and the battery was fine.
It has a charge "counter" device on the earth lead, a small black box right next to the battery terminal. If it thinks too much has gone out and not enough has gone in it will give this warning and cease the stop/start function.
I convinced mine that it was OK by connecting a spare lamp (motorbike headlamp bulb) directly to the battery terminals so it discharged the battery a bit but NOT through the charge monitor device, so it wasn't aware that charge had been drained from the battery. I probably drained around 8Ah from it, 4amps for a couple of hours. You don't want to flatten it.
I then used a charger, but you could just as well simply run the engine again, so it charged the battery back up THROUGH the charge monitor. This seemed to successfully convince it that more has gone in than had come out, and since then I've not had the battery icon and the stop/start works as intended.