BlueMail currently allows you to leave emails on the provider's server for POP3 accounts, as well as delete them in various circumstances.
Please go to More... | Various Account Settings | Tap on your account | Delete Messages on Server:
- Never - In order to keep emails on server (it is the default).
- When deleting from trash - Emails will be deleted from server when deleted from the Trash folder.
- When downloading messages - Emails will be deleted from server automatically when received.