This is the expected behavior of the conversations tool, and it's designed this way to ensure a more cohesive customer experience.
Each time a rep responds to an unassigned conversation, the email will be assigned to them and will stay with this rep until the conversation is closed. If the customer follows up, the conversation will also route back to the rep that assisted them to ensure that the customer doesn't get bounced back and forth with different reps.
Would you be able to tell us a bit more about your use case, please? Are you looking for a way to leave each of the customer's replies "unassigned"?