Observed influences of system response delay in spoken human-machine dialogues are rather ambiguous and mainly focus on perceived system quality. Studies that systematically inspect effects on cognitive performance are still lacking, and effects of individual characteristics are also often neglected. Building on benefits of cognitive training for decelerating cognitive decline, this Wizard-of-Oz study addresses both issues by testing 62 elderly participants in a dialogue-based memory training with a virtual agent. Participants acquired the method of loci with fading instructional guidance and applied it afterward to memorizing and recalling lists of German nouns. System response delays were randomly assigned, and training performance was included as potential mediator. Participants’ age, gender, and subscales of affinity for technology (enthusiasm, competence, positive and negative perception of technology) were inspected as potential moderators. The results indicated positive effects on recall performance with higher training performance, female gender, and less negative perception of technology. Additionally, memory retention and facets of affinity for technology moderated increasing system response delays. Participants also provided higher ratings in perceived system quality with higher enthusiasm for technology but reported increasing frustration with a more positive perception of technology. Potential explanations and implications for the design of spoken dialogue systems are discussed.