basically... yes the quality does suffer.
Every time you save a JPEG the compression algorithm is run on it to reduce the size, the first time the file is saved you can't really notice any difference, but each time it's saved after that it's compressed a little more so more quality is removed.
If you are going to be re-saving a picture lots of times due to editing it. you are best off to start with a uncompressed format and then just save it as a JPEG when you've finished editing it.