Are you using IMAP or POP3 for your email? I think you can only do that with POP3.
In your Inbox, go to More - Settings, then select the email account. When the settings for that account open, go down to the bottom and select Server Settings. Then, under Incoming Server, it will say whether it's IMAP or POP3. If it's POP3, you should have a setting there called "Delete email from server". Just select "Never".