That article, as well as a few others I found, points to not having enough processing power to handle the traffic. I'm sure that was relevant in 1980. Since article is from 2007, I think he was working with REALLY old hardware.
And I'm sure that packet logs carry very deeply hidden meta data which would make my problem trivial and a solution perfectly obvious, but I thought that posting the exact description of the ONLY TCP error messages that show up in the logs would be sufficient. Rest were RSYNC commands and actual data.
Workaround that solved my problem:
I solved my problem with an infinite loop and a timeout setting:
while true; rsync -az --timeout=10 --password-file=~/.psswd /media/Backup/ user@server::user/Backup/; do