Here are the steps to make your iPhone 5s, iPhone 6, iPhone 6+, iPhone 6s and iPhone 6s+ etc. check email automatically.
Step 1: click on the settings icon, then choose the Mail, Contacts and Calendars option.
Step 2: Click on Fetch new data option.
Step 3: make sure mail account is set to fetch not push.
Step 4: Under the fetch schedule make sure it's not set to manual but instead hourly, every 30 minutes or every 15 minutes, which is what I have mine set to.
Once your done you should be all set!