High power radio emissions near 2--3 kHz originating in the outer heliosphere have been observed by the Voyager spacecraft. Recent theories for these emissions combine acceleration of nonthermal electrons at global merged interaction region shocks with formation of a superthermal electron tail by lower-hybrid drive associated with pick-up ions, beyond the heliopause. This paper examines the efficiency of this process during the solar cycle, based on variations of the availability of pick-up ions in the source region associated with periodic solar cycle variations in the solar wind ram pressure. It is predicted that high levels of pick-up ions are present in the source region approximately 2--3 years after solar maximum, leading to strong emissions, in close agreement with the observed timing of events: the 1983--84, 1992--93 and 2003 events were preceded by solar maxima in 1980, 1990 and 2000, respectively. These results provide further evidence for the proposed model.