I experience this problem as well with my accounts from time to time. I have everything set to check e-mail every 5 minutes but it doesn't seem to always work this way. I have used the gmail app which is great for receiving notifications in a timely manner, but I'm not a fan of the way it looks. I prefer the way the device's regular e-mail looks better but the downfall is the sync doesn't always seem to work consistently, no matter what account is synched.