Here is a test from Practical Sailor showing the decrease in strength of nylon dock lines after cleaning:
http://cdn.practical-sailor.com/media/newspics/bleached_line.jpg
Practical Sailor usually does a pretty good job, but they sure blew it on this study - it's rubbish. The amount of chlorine bleach they used - 16:1 dilution - is ridiculously high. The suggested bleach dose in a homestyle washing machine is closer to a 350:1 dilution, or roughly 22 times less bleach than they used. I rather suspect that a single application of a normal dose of bleach would probably have close to the same effect as they saw for simple washing. But if you want to make things look dramatic, by all mean increase the dose.
That's not to say that chlorine bleach can't cause damage to fibers, because it can. But when used at the suggested dose it won't cause anything like this amount of damage.