E mail account settings
If you are using imap, that is how it works. When you delete a message on your phone, it is synced with the server and thus whatever you do on your phone is done on the server as well.
If you want the messages to stick around, have them forwarded to another email address like an outlook.com email and then set up the outlook.com email on your phone.
This is what I do. The nice thing about outlook.com is you can go to their site and set up your actual email address as an alias, so when you respond to an email, it will show your real email address as the from email and not the outlook.com address. You will also get the benefit of instant push email on your iPhone vs fetching at specified intervals.