Not sure I can help with the stuttering bit, but battery voltage is also monitored. When the voltage drops below a certain level on these systems, the engine will restart regardless of the other "stop" conditions being met.

As said. In wintertime, remember there is a lot greater load on the battery - lights, heated screens, etc. As such, a lot of people with auto start/stop cars tend to think the system is faulty in winter, because it never (or rarely) kicks in, or the car will just re-start itself for (seemingly) no reason.