No, a new request is not required, IF your DeBN account is still active AND if your name and address in the DeBN account and in the new case match exactly. However, if you change your name or address, the court will not be alerted to update your DeBN account UNLESS you submit a new DeBN request in your new case; if a new request is not submitted in these circumstances, you will receive service via U.S. Mail.
Generally, unless you deactivate your DeBN account (or the BNC or the Bankruptcy Court disable your account: see Can my DeBN account be deactivated by the BNC or the Bankruptcy Court?), it will remain active even after your case is closed, and you will continue to receive electronic notice of orders and court-generated notices in any current or future bankruptcy case or adversary proceeding from any bankruptcy court in which your name and address match the name and address on your DeBN account. This includes cases in which you are a creditor, plaintiff or defendant.