Stainless steel is relatively soft and easy to scratch. A mirror finish is going to show scratches more than finishes that are effectively "pre-scratched" for you like brushed or bead-blasted. The best advice would be to get used to the idea that your range won't look like new forever, although I know that advice is hard to take for some. Try to consider it a patina that comes with use.

You can't stop the process but you can slow it down if you want: clean less often (no cleaning, no scratching) and when you do clean, rinse your sponge or cloth more often.

Also you can buff it out with a rag and polish (tooth paste is mild and works) or rubbing compound. It depends on how deep the scratches are. Try an area that doesn't show. No good idea on how to avoid them except for what Markw suggests.