Solid rubber tires do not deflate. Unfortunately, solid rubber tires are not only much heavier than their air-filled counterparts, they don't absorb the shocks of riding on anything but smooth road, transferring every bump to the rider. Advances in technology and materials have produced airless bicycle tires that don't puncture while providing a ride experience comparable to standard air tube tires.
The first bicycle tires consisted of metal bands wrapped around wooden wheels. Solid rubber was the next material used, and although it improved upon the ride experience, tires with hollow centers began to appear and improve the experience even further. Since the mid-19th century, stronger rubber and other materials allowed for the use of thinner tubing, giving riders better control, less weight and a smoother ride.
The main disadvantage of air-filled, or pneumatic, tires is that they deflate. They tend to lose pressure over time, and they can be punctured, forcing the rider to fix or replace the tire before continuing. Small repair kits and liquid sealants are the most common solutions to this problem, although slime and other sealants placed inside the tube, either before or after purchase, seal off small leaks and act as prophylactics against punctures.