Why don't all of my emails appear on my phone?

My iPhone has stopped uploading emails unless the person is in my address book. But I am missing things like tickets to concerts and gift vouchers, and then find them on my laptop days later.

I am running a gmail account, and clearly its still working. Is this an operating system thing, or is it a setting in mail? I have been on heaps of forums to find clues: mail is nested under apps in settings for some reason. Help!