Q: Does dilution of bleach actually affect it's stability over time?

My wife buys these Chlorox variations, so I decided to ask
Chlorox (800-292-2200 & 800-227-1860) what the percentage of
sodium hypochlorite was in their two products pictured below:
http://www2.picturepush.com/photo/a/...g/12122385.jpg

The answer came back as follows:
a. 10% NaClO (pool bleach)
b. 2.4% NaClO (Chlorox Ultimate Care Bleach, UPC 44600-01692)
c. 2.4% NaClO (Chlorox Toilet Bowl Cleaner with Bleach, UPC 44600-00938)

When I mentioned my goal of using pool bleach, diluted to those
concentrations with tap water, they forewarned that diluting bleach
lowers its stability and effectiveness. Huh?

Specifically, they said that if I diluted 10% pool bleach, the resulting
solution would only be effective as a disinfectant for 24 hours.

Q: Is that true?

Reading the labels, they list "inert ingredients", but I have to assume
that the "inert ingredient" is plain water. Isn't it?