Just how light-sensitive is ethidium bromide?
Good question.

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.