This isn't a problem I'm currently facing, rather just a curious thought.
I know that every time you open and resave a jpeg it will lose information, How many time could you do this until there is a noticeable difference? 10/100/1000 times?
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I've seen a video featuring this. I'm not sure what it was anymore, but check out these 3 videos (from YouTube and Vimeo):
(The images aren't hyperlinked. Instead, there are linked texts at the bottom of each.)
I'm sure there are more out there.
There is no simple answer - each compression event dumps some data, it tends to dump less with subsequent saves as most of the disposable data has already been disposed of. Factors include the compression level, the size of the image, it's content, your personal threshold of "noticeable" and the quality of your monitor.
I once worked for a multimedia company where a graphic-artist was tasked with this exact question. Her findings were:
*distinguishable: to a 'normal' 'regular' human viewer, without magnifying the image.