It is possible to repair a toilet flapper by replacing the worn-out flapper with a new one. It is best to take the worn-out flapper to a local home hardware store to make sure that the new flapper is the same design as the old one.
Most toilet flappers wear out as bacteria in the toilet tub eats away at the plastic. However, there are toilet flappers, such as those that are manufactured by Fluidmaster, that come with an anti-microbial protection layer that prolongs the life of the flapper.
Toilet flappers are generally easy to remove and replace as most require nothing more than a screwdriver. Others simply pop off from the valve assembly. Many companies design generic toilet flappers that are advertised to fit any toilet, however it is best to buy a replacement flapper that is compatible with the specific toilet model in question.