I have 2 phone on which i use Avast. One is a LG Motion with android 4.0.4, the other is a Samsung admire with android 2.3.6. Neither phone has been rooted. On the Admire I keep having an issue where my email stops syncing. I checked my sync settings and the are all on but shows the day it stopped syncing. I have tried a few things with settings but the only way I can get it to sync again it by removing Avast Anti-theft. Once i remove it the email syncs and i put Anti theft back on. A few days later I notice that it stopped syncing again. I repeat the same steps to get it to work again and I am good for a few days again, I have gone through the process several times now. I have made sure is have the newest versions from Google Play Store. The LG Motion does not have this problem nor did my previous device the LG Esteem.
this seems to be a problem specific to your phone, as we do not modify any sync settings. unfortunately i think there is no easy solution to that. you can send me a ADB log maybe that gives more info (but i dont suspect so).
I updated the android os on the phone which essentially did a factory reset yesterday and then re-installed Avast and the few apps i use on this phone. I am not sure exactly what could be causing the email issue but it is not a constant problem, it works for a while then stops. I will send an ADB log if it happens again.