If a character fails a Constitution check while doing a forced march, they take 1d6 nonlethal damage and become fatigued. Eliminating the nonlethal damage also eliminates the fatigue. However, nonlethal damage recovers at a rate of character level per hour. Does this mean that a 6th level character can march forever?
In the section Nonlethal Damage in the subsection Healing Nonlethal Damage the Player's Handbook says
A forced march requires a Constitution check (DC 10 +2 per extra hour). Failure means the character takes 1d6 points of nonlethal damage and is fatigued, but a level 6 character heals this nonlethal damage (even if a 6 is rolled) in another hour, just in time to make another Constitution check. Further, "[e]liminating the nonlethal damage also eliminates the fatigue" that's caused by that failed forced march Constitution check (PH 164).
A perfectly reasonable house rule, however, is to insert the words of rest between hour and the second per and in that first sentence (i.e. "1 hit point per hour of rest per character level"), preventing characters of lower-middle levels from marching forever. It's equally reasonable, though, to just assume even lower-middle level characters can just forced march forever; it's appropriately cinematic, especially given that, by that level, wizards can fly, druids can use wild shape, and clerics can cure blindness, curses, deafness, and diseases.
While you could march virtually forever, it would be a slow, crippling walk after two failed Constitution checks.
While preventing the nonlethal damage from a forced march also prevents fatigue, taking the damage then healing it away is different, and does not remove the fatigue effect - removing fatigue requires 8 hours of rest.
The second failed Constitution check during a forced march would then make the character exhausted which halves your speed, and increases the amount of complete rest required to remove all such effects by a further hour.