I have a 6.0 that has an intermittent problem it runs bad every now and then. Hard to start it takes three times before it will stay running. Now it is shutting down while it is running down hwy.
Sounds like your FICM (Fuel Injection Control Module) is just about to die. What year and how many miles on your truck. The factory FICM goes out at about 110,000, and up, miles. You can get a rebuilt FICM here: ficmfixer.com This site also shows how to check that the FICM is bad. Do the test for your self and you will know for certain.
The truck is a 03 and has a little over 150000 it just started doing this in oct. and is getting worse as time goes on took it to a mechanic he hooked it up and that it showed the #3,5,6 injector intermittently stopped working
you can check the ficm your self to swamps diesel has a good tech artical on how to check your voltage. sounds like it could be the culprit on your vehicle shutting down.