Ok I know I read a thread about this a while back but I couldn't find it, so I just thought I'd post this up here if it could help anybody else out. From what I have read this has been an issue for many 6.0L owners.
I have a 2004 F250 FX4, and have had intermittent starting issues with the truck. Most days it would run fine, but occasionally I would try to start it and not a single noise would be made. I'd get it towed to the shop, and by the time it arrived it would be starting fine. Very frustrating, as this would only happen once or twice a month and typically worked fine before the mechanic could take a look at it. After about a year of this issue, it completely quit starting and the mechanic replaced the starter on it (with a Bosh starter) and it ran fine for about a year. Then all the sudden, the same issues. Neutral safety switches, sensors, and 7 starters later (in a matter of 3 months, each one more powerful than the last) the issue still persisted. Realizing that there was a bigger issue killing the starters, I took it to a transmission shop to have it looked at. They found that several teeth had broken off of the flywheel, which was causing the starters to burn up. New flywheel, and a stock sized starter and the truck has been running great ever since (been about 4 months now). I hope this can save someone the frustration I've had with this truck.
That being said, I'm over 200,000 miles on this truck and it's still running as strong as day 1.