Whenever I clean my grips I take a soft brush, dip it in water with liquid soap in it and scrub the grip all around.  It makes the grips very tacky and lasts very long until the next clean.

I bought a used Scotty Red X with the standard red small s grip. Tried cleaning with a mild solution of soap and water and good rinse. No luck. Took it to my local golf shop. The repair guy said the grip contains natural rubber so they tend to get hard, shiny, and slick. Swapped the grip with the same type. No problems for three years now and still good to go.

you could try rubbing it down with some sand paper but I would suggest a new grip and having it put on by your local pro, they will be able to put it on so the face is square ( do a better job than one could do in their garage)