Recent research has focused on developing non-task-oriented dialogue agents with high anthropomorphism, aiming to sustain users' dialogue motivation over prolonged periods. Previous studies have introduced chatbots that deliberately incorporate short response delays to enhance anthropomorphism and user satisfaction. However, in the context of long-term casual conversations, the behavior of these chatbots, which reply within a few seconds, may lead to a perception of the chatbot as always on standby, lacking its own schedule or personal life, thus appearing less humanlike. To address this issue, we propose a non-real-time chatbot that interacts with users while introducing deliberate response delays on a larger time scale, ranging from a few minutes to several hours. A five-day dialogue experiment confirmed that the non-real-time chatbot was perceived as more humanlike and encouraged users to engage in extensive dialogue. These insights are invaluable for designing chatbots that can maintain casual conversations over prolonged periods.