this isn't much of a fix and works just with gmail, could work with others too but I don't know what those apps would be...
anyways, I have an app that opens gmail like it does in a browser (just easier to click). This means I get the latests emails only when I open the app. No need for email checks, unless you want to read them offline :S
if you want to be notified of a new email, have gmail send you a text when you get an email
How To Setup Gmail SMS Alerts For Urgent Emails for Free