Or when you notice quality loss because the original JPEG has significantly higher quality than whatever it got transcoded to.
Seriously, people, stop transcoding to "newer, better" formats at lower quality. Just stop. I should never have a better experience if I set up an older browser that doesn't accept your newfangled stuff. Either manage to get the quality right (easier said than done) or just don't transcode stuff.
(This is much easier to get right if you are also shrinking an image.)