Dull tile can be cleaned using an electrostatic cloth. Several companies make electrostatic cleaning products that are similar to the Swiffer. For the environmentally concerned, 3M makes an electrostatic cleaning cloth that can be washed and reused.
For example, my basement was recently drywalled. As a result, microscopic dust has landed onto my ceramic tiling in the kitchen area leaving a dull film after many washings. I have washed it with various floor detergents, vinegar and water, to no avail. It looks clean until it dries and you can see this film leaving a dull finish. I have changed the sponge heads on the mop several times as well. What will cut this and bring my floor back to its natural luster?
I was recommending Gel-Gloss to polish the floor and eliminate the dull haze but I was afraid it could make the floor too slippery. You tried T.S.P. (trisodium phosphate) and the Dirtex I suggested, but they did not do the job. It was the Swiffer, from Proctor and Gamble, which removed the dust residue that was giving the floor the dull look.
The electrostatic cloth on the Swiffer that did what detergents and water could not have done. If you have not seen one it looks like a long handled duster with a rectangular pad wrapped in a cloth. It attracted the fine dust from the drywall and left the floor glowing.
Not only have I learned how to eliminate drywall dust, I now sell (and use) electrostatic cleaning cloths.