Did you try... oh, I dunno, *asking* yandex ? They have logs that can tell you what happens; you don't.
Yes, I did. ya-dump.cap was captured by yandex support. They told to me that have "conversation with mx.tehstroi.ru[81.25.172.91] timed out while sending message body" errors. Also they suppose that problem is on my side or on my ISP.