The shiny surface of new ceramic tile is a glaze that's baked onto the tile as part of the manufacturing process. Obviously, re-baking it isn't an option when that surface starts to dull with age, but there are other options. You can effectively reglaze tile by covering it with the same kind of clear liquid gloss that is used on wood floors. The gloss won't stick unless the surface is properly de-glossed to start with.
Dull the existing tile as much as possible with your belt sander, sanding across it tile by tile. Don't try to take the existing glaze off completely, but de-gloss it.
Mix 273 g (1 cup) of trisodium phosphate into 4.5 litres (1 gallon) of warm water. Scrub the floor with this solution, using a scrub brush. Rinse well and let dry for 24 hours.
Brush polyurethane floor gloss onto the tiles one by one, starting in the corner furthest from the entrance. Make the layer of polyurethane thin and smooth, covering the whole tile face but not the grout. Let the polyurethane dry for 24 hours.
Lightly sand the polyurethane with extra-fine sandpaper, dulling the whole surface. Sand it in light, small strokes. Wipe up the dust.
Brush on a second layer of polyurethane gloss with the same method you used to apply the first coat. Let it dry and lightly sand it.
Add a third layer of polyurethane in the same manner. Don't sand it, but let it dry for two days before using the floor.