You cannot use the fob to lock the doors while it is running, I believe. I will have to check this on my wife's Durango. It will stay running if you take the key fob and the evic will chime with a message saying the key has left the vehicle. But I don't know if it will let you remotely lock it. You may have to manually lock each door.
Can you use a 2nd fob to lock the doors and leave one in the vehicle? You have been able to do this in the past as I always have started my vehicle and locked it with another fob to warm up during the winter.
The keyless go would get annoying as my wife often leaves her purse in the truck when we go somewhere so I didn't get the keyless go. From the manual...doesn't state anything specific to a vehicle running.
Preventing Inadvertent Locking Of Passive Entry RKE
Transmitter In Vehicle
To minimize the possibility of unintentionally locking a
Passive Entry RKE transmitter inside your vehicle, the
Passive Entry system is equipped with an automatic door
unlock feature which will function if the ignition switch
is in the OFF position.
If one of the vehicle doors is open and the door panel
switch is used to lock the vehicle, once all open doors
have been closed the vehicle checks the inside and
outside of the vehicle for any valid Passive Entry RKE
transmitters. If one of the vehicle’s Passive Entry RKE
transmitters is detected inside the vehicle, and no other
valid Passive Entry RKE transmitters are detected outside
the vehicle, the Passive Entry System automatically
unlocks all vehicle doors and chirps the horn three times
(on the third attempt ALL doors will lock and the Passive
Entry RKE transmitter can be locked in the vehicle).