2011 Jetta randomly dies

A couple of months ago, my Jetta started randomly dying
while driving. The car will sort of seize up while I'm on the
road and eventually lose power. I can usually get it to
restart after a few tries and pushing down on the gas, but
it's terrifying when it happens in rush hour traffic. It also
has issues starting; I can get it to crank but not turn over
unless I play with it for 15+ minutes. When this happens,
the engine and battery lights come on but they of course
turn off once I'm able to get the car started. I've had
several people look at the car and even drive it but they all
say the car seems fine. I've also had the fuel pump
replaced but it still acts up. Any ideas on what it could
be? All help is appreciated.