Keep your timpani mallets in the plastic bags they came in, or other plastics bags. Only the felt part really needs to be covered. This will help to keep the felt from getting worn out and messed up.

Also, avoid touching the felt with your hands. This will help to keep the felt from getting dirty because oil attracts dirt.

You may even consider wiping off the timpani heads with a tissue before playing to keep oil from your hands from gettting on your mallets.