When US forces settle in for a long peace after fighting a difficult war -- as in (West) Germany and Japan following World War II, or South Korea since the 1950s -- their presence has generally nurtured stability, prosperity, and democratic freedoms. When they retreat precipitately — as in Lebanon or Iraq — renewed cruelty and violence predictably fill the vacuum.
There is a huge difference between the scenarios presented here where U.S. troops "settled in for a long peace" and those where they "retreated precipitately." In the case of Germany and Japan, those nations were effectively destroyed before any military occupation took place. And South Korea wasn't even an occupation as I would use the term (the U.S. didn't topple the Korean government in a military campaign).
The cases of Lebanon and Iraq, along with Vietnam, don't make the case for long-term military occupation at all. In fact, a better case could be made that the U.S. never should have had a military presence there in the first place. You don't fight a half-assed military campaign and then expect to get any results. You're better off if you don't even bother with the military campaign in the first place.
Must be a Ron Paul follower, right?