As Brangdon points out, probably 24 hours at most. Besides aquarium lovers, the typical microbiology lab handbook will tell you to toss out any diluted bleach solutions you mix up for disinfecting purposes fairly quickly. The times vary, but never more than 24 hours. So, say, 24 hours to have any sort of hope of killing any nasty bugs. You may still be able to detect it in the water after that point, but it would be useless.

I'm kind of bummed that I can't seem to find that bleach thread from a while back where I went into this topic in depth. I wonder where it went...

Pete makes a good point that any bleach in the water will be continually reacting with any organic matter. Although the lab example is a bit different since the animals are actively introducing organic materials by using that water lick device. However, as with benjammin's setup, if you had some sort of biofilm in the tanks, bleach could react with that.

Anyway, so that is one of the reasons many municipalities have switched from using chlorine to using chloroamines in their water supplies--the persistance over time.