Message doesn't update when iPhone turned off

I'm running El Capitan and use iMessages. I have iMessages set up to receive messages at both my iPhone number and at my email address. I've found that when my iPhone is turned off, I don't get messages on iMessage on my Mac. When I turn my iPhone back on, I can have several messages pop up on iMessage that were sent during the time the iPhone was off. How can I fix this problem?

-iPhone iOS is up-to-date with the lastest avilable version - 9.3.1.

Thanks!