iPhone 'steals' email from OSX mail
You should switch to using IMAP protocol instead or POP. IMAP has better support for multiple devices, and leaves the messages on the server by default. For more info on POP vs. IMAP here's a good link.

Note that you shouldn't just change the protocol, since a part of your messages has been downloaded to your device and deleted from the server. If you change the protocol, you may experience data loss. Instead, create a new account with IMAP and the same logins, and move the missing emails to the new account. After this, it's safe to get rid of the POP account and start using the IMAP version. For mote info, check this guide.