[Tsuwabuki]

Theoretically, a laser could go on forever. Lasers are light, and the light from a laser will continue to travel in a straight line until:

A) It is reflected.
B) It is absorbed.

It is far more likely that there is some sort of limit given background radiation and interstellar dust even in the fairly barren areas between solar systems. Such background "big bang leftovers" will eventually reflect and absorb all of the light until it is just scattered and no longer worthy of the name "laser." The closest we could probably ever get to knowing is by firing a laser out the galactic edge, and somehow trying to track it until it hits another galaxy. Assuming almost no interference in space from particles between galaxies (which is even more barren than space between solar systems), it is conceivable that such a laser could last, intact, for millions or even billions of years.