Although drill bits for concrete (masonry bits) are designed to bore holes into concrete, they are not impervious to wear and rust. With proper care and maintenance and adequate information you can keep your masonry bits sharp and continue boring holes.
Even when a masonry bit becomes dull from use, you can usually sharpen it if you have the right tools and skills. Drill bits are designed with edges that are not only sharp, but are slanted with the best degree of slant that will allow the bit to penetrate the material into which the hole must be made. In sharpening the bit, the key is to maintain this slant or angle. If you use a grinding wheel to sharpen your bit, you'll need to use the side of the wheel for sharpening the bit. With practice you can learn to hold the bit at just the right angle as the wheel cuts into the bit's beveled edge.
Your steel masonry bit will have a tendency to rust if exposed to moisture for long periods of time. Rusting will dull the bit and make it unusable. To avoid rusting you should first apply a light coat of oil to your bits using a dry cloth. Keep the bits in a dry place and, after using a bit, apply a fresh coat of oil.