One lab I was in was paranoid about keeping it in a foil-wrapped conical tube; my current lab leaves it out on the bench (and it works fine for staining gels). It's the same company/concentration in both cases, but this second lab uses it up much faster.
I found this reference in "Molecular Biology: A Project Approach"
A phenomenon called photobleaching occurs when ethidium bromide (EtBr) -stained DNA is illuminated by ultraviolet light.... This decreased fluorescence is presumably due to the dissociation of ethidium bromide from the DNA.
Ethidium bromide fluoresces when it is in a hydrophobic environment, such as when its stuck between two base pair stacks in DNA- water quenches its fluorescence.
I also found this article citing the fact that sunlight can break down EtBr but only when a catalyst of iron and titanium dioxide is there to catalyze the reaction.
A lot of the original characterization of EtBr as a stain is very old, so I couldn't access it directly online... It looks like the compound itself is pretty stable, but UV can, somehow interact with it when its bound to DNA to bleach it out.
In my current lab we just leave the bottle out (but use it up pretty quickly as we have 20+ people). But we do buy 5 bottles at a time and leave them in the same spot as the bottle that is in use (inside a hood, with the light always turned on) and we've never had a problem with degradation/expiration