This is an expansion of the experiments on JPEG that I reported in this post. It's worth reading that before continuing here.
This time I was looking to expand the idea to the limit - just how many iterations would it take to cause the image quality to break down?
I took the same image, working with Lightroom JPEG quality 75 and continued to successively expot the full size image. At the 35th iteration I found the first artefacts - pixel blocks, about 3x3 in size, in one of the dark patches. Nothing that would show up in print. In fact, it took a while to find it at all on screen at 100%. I then continued. At 80 iterations I got bored, happy that this is well past the number of successive saves I'd ever need.
I also tried an image that had been sharpened in the first conversion from uncompressed TIFF, using Lightroom's heavy screen sharpening. After 20 iterations there was no difference, apart from the sharpening - no artefacts, halos etc. I'd expect it to go many more iterations without problem.
I also devised a torture test, creating a multi-patch image with random detail running across it. This is a graphic image better suited to GIF than JPEG. Result: noticeable degradation around the wiggly line after 10 images at quality 75, but only against pure colour (one of the white patches and the pure green bottom left). The rest was intact, including edges between patches. The file size is small, reflecting the large colour patches: 340kB for a 6MP image, much smaller than the 1.2MB for the other, 10MP image.
Final conclusion on using JPEG for presentation and book making: I'm sticking to lower quality levels than before, using JPEG exclusively for creating photobooks and not getting too worried about compression settings.