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I encountered the same problem as well. i found that Avast’s proxy does NOT work well with ssl under certain circumstances, such as when Apple mail client try to establish connection via ssl.
The simplest solution to resolve that is (only my option) to tell avast mail shield not to scan secured connections.
To do that, open avast preferences, click “advanced…” on the right side of mail shield,
in general page, uncheck “scan secured connections”.
I would rather take risks than miss all incoming mails.