Try cleaning the tile with a good clarifying shampoo (I used Prell) and a nylon bath net for showering. Do this immediately after taking a nice hot shower. Be sure and rinse/dry well afterward.

Once it is clean and dry, use Gel-Gloss on the tile, this will help keep bath soap from sticking.

Bar soap leaves a residue on tile, be sure and only use a liquid bath wash.

Be sure to rinse and squeege immediately after taking a shower.

I would guess that the finish on the tile has been etched by using strong cleaners. I had tile that was etched from shower cleaner.
I would suggest wax....or perhaps that product you use on car windshields to keep water from spotting...Rain-X is one brand.
Linda C

It sounds like it might be caused by hard water deposits or calcium build-up.

Do you also have a glass shower door, and if so, does it have build-up at the bottom?

I'd suggest you trying different suggestions for cleaning glass shower doors, and trying them in a small inconspicuous spot in case they might do further dulling.

Sue

These are all great ideas. We don't have glass shower doors. It may be hard water as suggested. We got a water softener but not until about 10 years ago. Tile has been dull for longer. I have tried some things off and on, but will give the suggestions you all made one at a time! Also, no more bar soap...even if it is free when you bring the leftovers from motel stays. I always wondered if they just throw out all those little hardly used soaps....back to topic.... It's frustrating because the rest of the tiles are in very good shape. I'm a seasoned citizen and not interested in putting a lot of money into new bath.