fuel problem? help!!!

[nyfarmer87]

I've got an early 99 f250 7.3 that has me puzzled. It starts fine and idles fine if you don't let it idle for more than 20 minutes. If you do it acts like I loose half the injectors minus the white smoke. When it happens if you let it sit for a couple hours it runs fine again and runs with no problem. I have ran an injector test haven't had any codes pop up. Would it be my hoop or something else?