If the mitt starts to lose its grip capacity the first thing to do is flip it over!! You can always use the other side of the mitt! After that, you may need to wash the mitt with warm, soapy water and pat dry to renew the tackiness.
The reason the mitt gets dull is that it is picky up dead skin cells and cellular debris. In this case, you might want to consider the moisture level of your skin. Are you hydrating your skin enough? You might want to consider upping your water intake. In general, we should be consuming 1/2 our body weight in ounces of water per day!
Also consider using a good quality lotion to help hydrate your skin. Avoid lotions that are greasy. You don't want to use the mitt on greasy or oily skin. Consider lotions that don't have fragrances, as perfumes can be drying to the skin. Also check the labels on the back, if alcohol is one of the first 3 ingredients, ditch it!! Petroleum is an ingredient that can help keep the skin moist, but is best if it is the 3rd or 4th item listed under the ingredients.
Some really great options for extra dry skin are: Eucerin or the Equate brand, Aquaphor, goats milk lotion with essential oils, Lindi skin, lymphoderm, Amlactin, Curel, Nivia and coconut oil.