The mats are one solution, but in big league ballparks they use clay. There are 3" by 6" clay "bricks" (Moundmaster) that you build under your top layer. You can buy them by the pallet from places like Tomark.com.
http://www.tomark.com/BaseballStore/pro ... Amendments When you get a hole in front of the pitchers plate, just sweep off the top layer, moisten some loose clay and smoosh it together. Recover with the top layer and voila' you are ready to go. You have to keep the clay moist by watering regularly.
For more info, search on groundskeeping, field clay or soil amendments.
I built an area in my backyard for my DD to pitch including a hard cover. It was alot of work, but it is always ready to go.
The reason you get the pitchers hole on most fields is that it is just dirt. It will never fill in. Think of a sand box, no matter what you do the surface is always soft.