It is fermentable, of course, so if you can keep it refrigerated it will last quite a long time. You could also purge it with co2 to help make it last. Or just brew again very soon!
I was told by the owner of my LHBS who also runs a brewery to keep it in the fridge. That said I have some that's been in the fridge for about 6 months an it's still fine. Hopefully someone with more experience with LME will chime in.
I worked at a lhbs for a while. We had bulk breiss lme and it would start molding after about 1.5-2 months out at room temp with no co2/nitrogen purging of the headspace in the big carboys. In the fridge you could probably keep it for a year. Maybe more, I haven't tried.
