On the 2011 there is a starter relay that is in the TIPM module, if I remember correctly the relay isn't servicable and if it is defective would require entire TIPM to be replaced. There is a fuse for the relay (I think its 40amp) that might be defective, so that's something cheap to just replace.
I assume you haven't been able to duplicate the problem at the dealership, so they don't know what the problem is?
If you have someone to help you and have a 12 volt test light, you can try to trouble shoot it a bit the next time it starts acting up. Next time you hear the click and it doesn't start, open hood of truck, and remove the starter relay fuse. Removing the fuse will guarantee engine won't actually crank, and is for safety reasons. While someone tries to start the vehicle, use the 12volt test light (or a volt meter, either will work) and check if you have power on either terminal of the socket for the fuse you removed.
If you don't have power on one of the socket pins, then it means either its a bad relay in the TIPM, something in powertrain control module, or something else upstream of the TIPM. If you do have power then it means something might be wrong with starter or wiring to the starter or battery.