People living with dementia are at risk of social isolation, and conversational AI agents can potentially support such individuals by reducing their loneliness. In our study, a conversational AI agent, called MindTalker, co-designed with therapists and utilizing the GPT-4 Large Language Model (LLM), was developed to support people with early-stage dementia, allowing them to experience a new type of “social relationship” that could be extended to real life. Eight PwD engaged with MindTalker for one month or even longer, and data was collected from interviews. Our findings emphasized that participants valued the novelty of AI, but sought more consistent, deeper interactions. They desired a personal touch from AI, while stressing the irreplaceable value of human interactions. The findings underscore the complexities of AI engagement dynamics, where participants commented on the artificial nature of AI, highlighting important insights into the future design of conversational AI for this population.