Welcome to Android Forums and the Rezound area. Have you checked how often you have your two mail accounts syncing? Perhaps they aren't looking for new mail very often. I do not use Juice Defender and would advise you to discontinue it's use. I'm not knocking the app as much as I'm knocking a battery conservation program. It's pretty much accepted knowledge that the battery saving programs on the modern Android phones use as much power as they save. The OS is now designed to manage the power usage and yet let the phone operate as designed.
If you must use Juice Defender, you might try disabling it for a few days to see if it's your email culprit. In the process you can check your power use and decide if you really want to keep the app.
I hope this will help your email problem. If not, perhaps another will chime in with some other suggestions. I hope you enjoy these forums and they serve you well.