You should be able to see why it isn’t stopping in the menus. I think it’s under Trip/Fuel -> Auto Stop/Start. Mine has shown low temp and vehicle charging before.
If you received a PCM update, it is normal until the engine reaches temp and stays there for a short time. A 10-20 minute drive should get it back to cycling normally again.
My truck has 5000 miles on it, auto start stop quit working for 2 weeks roughly and started seeing some bugs in the truck. Warranty battery replacement fixed it. mine is a 5.0 but I've read all the threads on the bugs with a low battery so the dealer looked at me like an idiot when I told them I had a bad battery. Put a meter on it if you have one before you start it for the day. Mine was holding at about 11.95volts. No bugs since battery changed.
Seems the auto start n stop is wonky on my brand new 23' 5.0. I don't care for it anyway, but sometimes I forget to turn it off and when I realized it, it wasn't working anyhow during my travels. Then sometimes when I stop, it works. I'm like WTF, not consistent at all.