Mustang does not start when I sit in it too long?

My Mustang GT will go dead when I sit in it too long?  When picking up my
son from school I often sit in a car line for 15-20 minutes.  When trying to
restart the car it is completely dead, won't start, the key fob is unresponsive,
no lights, nothing.  If I exit the car and walk away my Mustang will often restart.  
Curious if anyone has this issue or what could be the problem?