Sorry about this.
Did you change the app's settings recently?
I could investigate if you collected a debug log (as below), with "raw session data" enabled.
I'd need the log to capture your refreshing (checking mail in) your accounts, at the very least -- or maybe you could leave the app running in the background for 2-3 hours (exiting its UI with the Back key).
This can be done on WiFi, which hopefully does not have a limit like your mobile plan.