It seems that sometimes AquaMail hangs up in a loop while checking for emails or synchronizing with Exchange account and consumes all the energy of the phone! I wanted to upload an image of the battery usage, but the forum wont allow me to do it.
The picture says that AquaMail consumed 59% of the battery, followed by the screen with 27%, and the Android-System with 19%, Facebook 17%.
Something goes wrong here if an email app consumes more than Facebook and even more than the screen and all other applications together!
I am on a Samsung Note 4 with the latest Android update.