Declining Industry
An industry where growth is either negative or is not growing at the broader rate of economic growth. There are many reasons for a declining industry: consumer demand may be steadily evaporating, the depletion of a natural resource may be occurring, or there may be the emergent substitutes because of technological innovation. 
Investopedia Commentary
An example of a declining industry is the railroad industry, which has experienced decreased demand - largely due to newer and faster means of transporting goods (primarily air transport and trucking) - and has failed to remain competitive in pricing, at least in relation to the benefits of faster and more efficient transport provided by airlines and trucking services.
Related Links
Industry Handbook
The Stages Of Industry Growth
See also: Business Cycle, Cyclical Industry, Emerging Industry, Growth Industry, Industry, Industry Bet, Mature Industry, Sunrise Industry