Why are new emails being threaded to the same case?
Salesforce relies on email threading (https://help.salesforce.com/s/articleView?id=sf.support_email_to_case_threading.htm&type=5) to ensure new incoming email messages are added to the correct case. For more information on how Email to Case Premium respects all threading behaviors, please refer to this knowledge article https://kb.vicasso.com/?kb=000004499.