Why are my non-gmail notifications delayed?

I just recently bought an LG Fortune 2. I soon realized that I was getting notifications for some of my emails, but not others. I have a gmail account and discovered that when I received emails from other gmail accounts, I received a notification immediately. But when I received emails from any other type of account other than gmail, the notification was delayed, and sometimes I never got one at all. I sent the phone back and got a new one, but I still have the same problem. It's very frustrating!

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