What are the settings for your mail delivery?
Mine are set for 15 minutes.
Perhaps that is the delay.
Go to mail - settings- send & receive- down load frequency

 

Settings > Wireless & Networks > Mobile Networks > Enable "Always on mobile data"

If this is not checked, certain items will come in randomly, typically a function of another app polling for data. Certain apps bypass this setting and force data through anyway. When this happens, it'll also push through things that ARE affected by this setting. If that doesn't happen however, when you wake the phone like you did, the data will come through at that time instead.

Could be wrong here, but I'm guessing your "always on" is currently unchecked.

 

A fluke, poor coverage at the time, IDK. Doesn't make sense to me with your current settings. Shouldn't be happening, especially with texts. Emails can be set for certain poll intervals depending on the app in use but texts should be coming through.

 

I've had the same problem since I brought the phone when they first came out. Well, I have the delay on emails but not texts. No one has been able to solve the issue for me. It must be some kind of hardware issue that's rare because not everyone has this problem. I'll get emails anywhere from instant to 15 minutes or so late.