Using counterflow combustion as a model problem, the structure and extinction of heterogeneous diffusion flames with radiative heat loss from the condensed fuel surface have been studied via activation energy asymptotics. The analysis yields solutions for the flame temperature, mass burning rate and the flamefront standoff distance, as well as the structure equation for the reaction zone which is identical to that of Linan previously analyzed for situations which are either globally adiabatic or subjected to radiative loss from the flame zone. The system also exhibits the dual extinction turning point behavior, in which flame extinction can occur not only for sufficiently large stretch rates but also for sufficiently small values as a result of excessive heat loss and thereby flame weakening. Consequently there exist systems for which steady combustion is not possible for all stretch rates. Similarities and differences of the present situation with other diffusion flame systems are emphasized.