Rather than answer the question directly with a haphazard response of, say, 50 years, let's see if we can go through a couple of basic conditions and see if an answer.
1. The United States has no business whatsoever enforcing U.N. resolutions, no matter how egregious the violations of these resolutions may seem. The U.S. will take military action when it sees fit to defend itself, regardless of whether the U.N. supports us. So scratch that one off the list. (It's worth noting, however, that for some reason, many conservatives who rightly bad-mouth the United Nations on a regular basis somehow consider "enforcement of U.N. sanctions" to be a legitimate rationale for war in this case.)
2. The last 12 years cannot be considered a "period of failure," since nobody seems to remember what the original goal was. This is precisely why nothing has happened there for 12 years -- the stance taken by the U.S. with regard to Iraq changed along these lines: a.) The U.S. is not concerned with long-running disputes between Arab nations (the infamous April Glaspie meeting with Saddam Hussein in 1990); b.) The U.S. must send thousands of U.S. troops to the to prevent Iraq from invading Saudi Arabia ("Operation Desert Shield"); c.) The U.S. military must now be used to enforce U.N. resolutions ordering the removal of Iraq from Kuwait ("Desert Shield" magically becomes "Desert Storm," though only a few of us began to wonder if we were getting our chains yanked); d.) Saddam Hussein is a madman -- the greatest threat to human existence since Adolph Hitler -- and therefore must be dealt with immediately; e.) Well, maybe he's not such a bad guy -- after all, how else could we explain why he was left there in 1991?; f.) On second thought (or third, actually), he's still a pretty bad guy but not bad enough that we have to do something about it. But we will actively work to encourage other groups in Iraq like the Shiites and the Kurds to rise up against him; g.) Oh, no. Those Shiites and Kurds actually thought we meant that last comment, and now they are rising up against Saddam Hussein! But rather than do anything about it when the Republican Guard violently quells those disturbances, let's establish a silly "no-fly zone" over northern and southern Iraq, and send U.N. weapons inspectors to find weapons of mass destruction.; h.) etc.; i.) etc.
(Note: Any possible connection between the first item -- "the U.S. is not concerned with disputes between Arab nations" -- and the last -- U.N. weapons inspections -- is strictly a coincidence. I can't imagine any other connection between the two.)
Now that we've made two basic points here, there are two answers that jump out at me. At your suggestion, I'll round them off to the nearest half-century.
First Answer: Zero.
This is the answer to the question when the U.S. is responding to a direct threat to our existence. The U.S. has no business screwing around with an enemy for even 12 months, let alone for a period of time that is twice as long as the second World War. 12 weeks may be a legitimate goal for any military action of this sort, though most countries wouldn't even last 12 hours against our military might.
Second Answer: One, and counting.
This is based on the precedent that was set the last time the United States launched a large-scale military campaign on behalf of the United Nations against a nation that didn't represent a direct threat to us. In the case of Korea, we're probably seeing the first case in the history of the world in which soldiers who are enforcing a cease-fire will be able to trade stories with their great-grandfathers who served as the first rotation enforcing that cease-fire.
c.) The U.S. military must now be used to enforce U.N. resolutions ordering the removal of Iraq from Kuwait ("Desert Shield" magically becomes "Desert Storm," though only a few of us began to wonder if we were getting our chains yanked)
That's one way to look at it, I suppose. Another way is to say that we were responding to the leader of a rouge state with an explicitly stated intent to draw as much of the Arab world as possible into a facistic and militaristic dictatorship, who already controlled (with Kuwait) nearly a quarter of the World's oil supply, and was imminently planning to control half (with Saudi Arabia).
Given the economic and strategic importance of oil, this was hardly a gratuitous interference in "disputes between Arab nations." But, hey, we could follow your prescriptions. We could wait for a palpably present and active threat to fully materialize. Then we could have a nice old-fashioned World War, with tens (or hundreds) of millions of dead, just like our grandparents did. Think of all the wonderful movies and posters our own grandchildren (assuming we have them) will be able to enjoy!