Eventually, the fish will die. Now, why the fish isn't eating could be a bunch of different causes. Have you tested your water quality? Poor water quality can stress the fish and cause him not to eat. He could also be sick. Do you notice anything different about his physical appearance? White slimy patches, red sores, or little white dots? What temperature is the water? The cooler the water, the slower his metabolism will be. Bettas are from a more tropical climate. Naturally, they tend to prefer warmer water. It could also just be that he doesn't like the food he's being offered. Try giving him different foods (pellets, bloodworms, flakes, small snails, and so on). He may be a picky fish.