I went through all the same issues you guys are currently having. I used K-9 for a long time and tried Maildroid. I finally switched everything to the Gmail app. Below is a writeup I did for a battery saving thread, but it gives the details of how to use the Gmail for all your email needs and save some battery.
Emails: I don't know what email app you use, but try this. It saves battery power and in some cases emails arrive quicker. This scheme will have you using only the Gmail app on the phone for all email accounts whether they are pop3 accounts or Gmail. Go to the Google Gmail inbox on your computer and log into the Gmail account. On the top right of the screen is an option called Settings. In there is an option to have the Gmail program poll your regular, non-Gmail accounts (From the inbox; Settings/Accounts & Import/ Check mail using POP3). Provide the email address and the password. The Google Gmail program will then poll your other accounts on a frequency from 1-5 minutes and push the email immediately to your phone. The polling frequency is determined by each account's activity - more emails = faster polling. This saves battery power because on the android OS pop3 accounts are polled at a frequency of 1-30 minutes and that really eats battery. Because the phone goes and checks those accounts for mail whether there is mail there or not.