How long would an artificial atmosphere on the Moon last?

An article here gives us a clue. The article itself is about a silly bit of opposition against the idea of  "bombing" the Moon again - before LCROSS hit the surface of the Moon there was a fair amount of opposition to this as some thought that it was a real bomb, that it would knock the Moon out of its proper orbit and a variety of other silly theories. In reality it was just a probe and a piece of a rocket that slammed into the Moon, and the impact was nothing even close to what the Moon has experienced during its lifetime and also experiences every few years or so.

As for the idea of an artificial atmosphere, the article has the following quote:

McKay added that "a real issue for scientists is the creation of a temporary atmosphere [on the moon] due to rocket exhaust. I've seen estimates that it would take decades to subside."

The fact that the Moon is not massive enough to maintain an atmosphere of its own in its proximity to the Sun is well known, but what is not well known (or simply not considered) is that this doesn't mean that any gases on the surface of the Moon will simply fly off the next day; it's actually a process that takes quite a bit of time and as the article shows even a tiny bit of rocket exhaust takes that long to get blown away. A tiny atmosphere similar to that of Titan that I've proposed here would probably remain for a few centuries.

As for whether an atmosphere on the Moon is a good idea or not: assuming we are planning to truly settle the Moon it's probably inevitable anyway. Having people on the Moon means rockets will be going back and forth between it and Earth, humans will create and use hydrogen and oxygen and other materials, will grow food, and so on, and there simply isn't any way to prevent the creation of some sort of atmosphere. Because of this it will probably be best to create a thin one that helps out in preventing impacts from the smallest of micrometeorites, regulates the temperature a bit and is able to help move the lunar dust around in order to dull its sharp edges a bit.