Verizon Iphone 4s (32GB) alerts not working correctly

Hi, I have a Iphone 4s (32GB) that i got at a verizon store this past summer (May-Aug 2012). I'm currently only using 7.3GB of it (so i don't really have a ton of stuff on it), and i always close my apps after i use them.

I am having an issue with the alerts. In my settings i have the notifications for imessages/text messages, and mail to be 'on' with Alert as the Alert style, badge app icon on, show preview, view in lock screen, etc on. BUT whenever i will get emails it will viberate once, but the email wont pop up as an alert, i will manually have to go to my mail to see what it is. Also, with text messages i can get a text message and my phone wont even viberate or send me an alert for it, i will just randomly have a 1 on the messages icon.

Is there a recall or something that would explain why my phone is doing this? I am puzzeled, because i take really good care of my phone and am confused why this would be happeneing- because i do all the right things to keep it working for as long as possible.

Thank you!