The critical point in working with JPEGs is when they're saved. Successive edits of the same file, in whatever processing software, without saving will not affect the quality. It's only when they're save that compression is applied, and it's the compression that reduces the overall quality. I've read that more recent versions of Photoshop are able to differentiate portions of JPEG files that are edited from those left unchanged by an edit, and that only the edited portions of files are subject to additional compression and therefore additional quality drops from earlier versions (I don't know whether this info. is actually correct, but that's the Internet for you).