If the messages are being deleted from the iPhone and the computer then you have set your mail account up as a IMAP account. Those accounts keep the devices in sync - an action on one will reflect on another one. (A delete on the iPhone will also delete on the computer.)
It sounds like you need to set up your mail as a POP account. That way actions on the phone will not reflect on the computer (Deleting from the iPhone will NOT delete from the computer.)
You'll need to inquire with your mail provide as to whether they support POP and what the necessary setttings may be.