I have the same result on my 2012 connie .
When the bike is cold (first started), like most bike engines, it will be prone to dying. If the idle is set too low or you do not wait a minute or two and take off but without enough throttle, it can and will die and I don't find that to be terribly alarming. If there is too much play in the throttle cable, this can amplify the problem, since a twist to give gas might not be quite enough. If you ALSO use ECO mode (which I don't bother with) that will tend to make the idle even less strong, even if the RPM is a bit higher, because the bike is then cold AND even leaner than normal.
I will admit that my 2011 has never died when leaving after cold started, but I almost always start the bike and let it run a minute or two before leaving. It is part of my routine- I am not finished preparing to leave before I start the bike. I will usually start it, and then put on my helmet, plug in my earphones, and put on my gloves and set the GPS/music options, and then leave. I consider this a "best practice". It is "better" for most engines to let the oil get a little up to temp and flowing through everything before calling for power.
A few times I have killed the engine, especially when the bike was new and I was slow manuvering, and I had too much play in the throttle. Once I got more used to the bike, and also removed the throttle play, it was never an issue again.
