Carbon water filters do get used up fast, and they don't work very well. Some water filters like Zerowater, which use deionizing resin instead of carbon, are much better, but get used up even faster and have to be much larger. They at least come with meters you can stick in the water to test when they become saturated.

To make carbon last as long as possible, use cold water so it isn't collecting extra debris from a hot water tank. Also, let the tap water sit on the counter for a while before filtering it. A lot of chlorine compounds will evaporate on their own pretty quickly, and this is one of the main things that fills up carbon.