Dogs are not marble's best friend. They lick themselves all over and wet themselves when they urinate. All of these acids along with normal traffic eat the polished finish right off the marble. You can't wipe an acid etch away.
My suggestion to you would be to have the floor rehoned. This involves the use of a buffer or heavyweight floor grinder equipped with diamond pads or abrasive stones (the best). I would bring the floor up to a satin finish and seal it with a mineral spirit based silicone sealer. Polished marble is difficult to maintain on floors and a satin finish is much more natural looking. In addition it will hide minor flaws caused by acid etching the surface and scratches will not be as noticable.
A temporary solution would be to have your floor recrystallized. Generally this is recommended every 6 months to a year for polished marble floors.