I'm not a mechanic by trade, but a computer engineer. Honestly, it sounds to me like an electrical or computer issue. I would still take it to the dealer and ask them to look at it. A 2013 should still all be under warranty.
2013 Mustang V6 w/Premium Package, Comfort Package (Yay pony lights...), Appearance
Mods: Airaid CAI, Ford Racing 3.73 Gears, Aluminum 1-pc driveshaft, American Muscle Staggered Black Bullitt 18" wheels, Bama Tunes, Ford Performance engine cover, JLT Air/Oil Separator, Boss 302 Strut Tower Brace