Check Fuse #47 in the underhood fuse box, or better yet just replace it. I once had an issue where once the car got hot, the engine would just shut off, even at speed. Throw it in neutral to keep it rolling and it would start right back up with the key. After doing that for awhile, it started to refuse to start back up even when it had cooled off. The fuse must have had a tiny crack in the beginning which expanded when it got hot, breaking the connection. There was no obvious evidence of the fuse being bad until the point where it would not start back up - that's when a teeny tiny burn spot became visible. Replaced the fuse and it has been fine for months now.
2009 GT , Brenspeed B326, Stage 1 heads, E-Force - 633 rwhp / 623 rwtq
2016 Ecoboost Premium, Bama Tune, JLT CAI, CPE Charge pipes, Mishimoto Intercooler, Tial BOV, Turbosmart 10psi Wastegate Actuator, 3" Downpipe, JMS Boostmax & Pedalmax, FRPP Borla Touring Axlebacks