How many emails do you have in the folders that are synced with gmail? If it is a very large number, have you considered moving older ones to an archive local folder, perhaps annual in and out or something like that, and then backup those folders. Then reduce the pressure on the synchronization process for both your computer and google.
In the olden days, long long ago, we figured we needed to clean out any active folder with more than 500 emails in it. This was not with emclient, but with other email programs. But even though things are much better now, thousands of emails are probably difficult to keep in sync, and unnecessary if many are years old.