An open relationship can last as long as the two people involved want it to. The issue is that often times one of the people in the relationship reach a point where they no longer really want that type of relationship. Once that happens the open relationship is not going to last.
The strength and quality of relationship, open or not, depends on the people involved with it. Like with any other relationship, an open relationship would require free-flowing communication between the people involved in it. Communication must be present for there to be trust among the people in the relationship. This is not to say that trust is not important in "regular" relationships, but in an open relationship, the issue of trust is even more paramount.
I think it depends on the people involved, but I think it is possible for an open relationship to last as long, if not longer than a closed relationship. One of the leading causes of marriage breakdown is infidelity. If the couple has accepted this risk, by having an open relationship, this would not cause their marriage to fail.
Open relationships can definitely work for people if they are entered into openly and with a full discussion beforehand. An open relationship, where two people share the same values and decide to enter it on their own, will work because there is no animosity there, so it is like any other relationship.
I do not think that something such as an open relationship can last between couples. I think the idea is a foolish one and is only practiced by couple that do not seem to respect and love each other that much in the first place. That is why there is a lot of case where such relations do not work.