I've often wondered, if I load a compressed image file, edit it and the save it again, will it loose some quality? What if I use the same quality grade when saving, will the algorithms somehow detect that the file has already be compressed as a JPEG and therefore there is no point trying to compress the displayed representation again?
Would it be a better idea to always keep the original (say, a PSD) and always make changes to it and then save it as a JPEG or whatever I need?
When it comes to lossy compression image formats such as JPEG, successive compression will lead to perceptible quality loss. The quality loss can be in the forms such as compression artifacts and blurriness of the image.
Even if one uses the same quality settings to save an image, there will still be quality loss. The only way to "preserve quality" or better yet, lose as little quality as possible, is to use the highest quality settings that is available. Even then, there is no guarantee that there won't be quality loss.
Yes, it would be a good idea to keep a copy of the original if one is going to make an image using a lossy compression scheme such as JPEG. The original could be saved with a compression scheme which is lossless such as PNG, which will preserve the quality of the file at the cost of (generally) larger file size.
(Note: There is a lossless version of JPEG, however, the most common one uses techniques such as DCT to process the image and is lossy.)