we've had our 2006 sonata in the shop twice because it will stall while driving at all speeds.it seems to happen more of warmer days. they can not find anything wrong with it. after about 5 to 10 minutes it starts back up. today i had to have it towed because it wouldn't start back up and a friend who towed it said it was a vapor lock and the gas lines should be reran to correct this. the warranty is up in november so i need to get it fixed. hopefully, someone has some ideas.

 

I think the first place to start is to scan the PCM for DTC, hopefully logic has seen something outside parameter and set DTC for the circuit..

Report back with results of scan,,, did it start with this fresh load of fuel ? Drive it out and try different fuel.