elec problem with 2008 Mustang

Measure the voltage at the battery terminals with the engine running. It should be somewhere between 13.5 and 14.6 volts plus or minus a tenth or two. If it is less the alternator is not charging. The ECU tells the alternator to start and stop the charging. If it is not charging the wiring needs to be checked at the alternator and the big wire should be hot to the battery positive even with the key off. It sound like the battery is draining and shutting off the car. Also check the battery connections at the battery and at the starter. These connections need to be clean, free of corrosion and tight.