Bad egr valve. Clogged with carbon. Cold a egr valve partially clogged will allow cold eg's pass(because there are not as many hot gases), but once it's hot it will stick open and you will get a lean fuel mixture and no start issues, along with poor performance. F250's with power stroke engine from 1999-2005 had all kinds of egr valve issues. Clean your egr valve and you should notice a difference.
Franco