Simple fact is, the battery has been recharged at the dealers a couple of times and the car has behaved the same way afterwards. Start-Stop begins restarting the engine after a few seconds, after which it doesn't engage at all. As this happens during one journey, and with no ancillary items such as AC or rear heater in use, it's reasonable to suspect that Start-Stop has drained the battery below a system-set threshold beyond which it is inhibited. The fact that the battery has maintained sufficient charge to operate the car for several months afterwards suggests that there's no underlying fault in the charging loop.