Recent developments in robot technology have led to the creation of multiple autonomous robots that are expected to perform tasks continuously over large areas. Particularly, continuous cleaning tasks are necessary for efficient maintenance of environments. Such tasks are expected to involve prevention of the abandonment of garbage. As described herein, we propose an efficient solution to the multi-agent continuous cleaning problem, overcoming issues inherent in the Probabilistic Dust Accumulation (PDA) learning-based goal determination method used for an earlier study. In that earlier study, random and repulsion methods were often selected for early stages of the problem when learning about dirtiness was in adequate, resulting in refuse being left unattended. Therefore, we introduce the “abandonment-priority random method”, which selects targets from a group of nodes that have not been cleaned for a long time. For the repulsion method, we also introduce the “abandonment-priority repulsion method”, which selects targets based on elapsed time and based on distance from other agents. Results of evaluation obtained for the experiment environment confirmed that combining the abandonment-priority random method with the abandonment-priority repulsion method improves cleaning efficiency in all experiment environments, particularly during the first half of the learning phase, when learning is still ongoing. This finding suggests that considering the passage of time is an effective means of improving multi-agent continuous cleaning efficiency.