If you use Gmail, you can blame Google. They took away Push for Gmail in the Stock Mail app. It uses fetch. Go to Settings>Mail,Contacts and Calendars >Fetch New Data >Scroll down to set fetch to your choice of the time. I set mine to one hour. So my mail comes every hour and alerts me each hour. You can set it to every 15 minutes, every 30 minutes, every hour, or manually. If it's set to manually, it won't do anything until you open the mail app.
Follow my directions and set here:
Sent from my ancient but trustworthy iPhone 5.