Found out in logs on the server that SFTP subsystem can not be found.
# journalctl -f
Jan 24 16:45:43 mysrv sshd[2045]: subsystem request for sftp by user XXX failed, subsystem not found
Don't know how it was disabled, but re-enabling it in config solved the issue.
Just uncomment one line..
# nano /etc/ssh/sshd_config
Subsystem sftp /usr/lib/openssh/sftp-server
Don't forget to restart the SSHd.
# systemctl restart ssh
Just for search engine bots - here is the successfull SCP log:
Authenticated to mysrv ([88.88.111.11]:22) using "publickey".
debug1: channel 0: new session [client-session] (inactive timeout: 0)
debug1: Requesting no-more-sessions@openssh.com
debug1: Entering interactive session.
debug1: pledge: filesystem
debug1: client_input_global_request: rtype hostkeys-00@openssh.com want_reply 0
...
debug1: Sending subsystem: sftp
debug1: pledge: fork
scp: debug1: Fetching /home/XXX/dir/app.rb to app.rb.bak
app.rb 100% 38KB 297.3KB/s 00:00
scp: debug1: truncating at 39240
debug1: client_input_channel_req: channel 0 rtype exit-status reply 0
debug1: channel 0: free: client-session, nchannels 1
Transferred: sent 3248, received 42336 bytes, in 1.3 seconds
Bytes per second: sent 2528.5, received 32958.1
debug1: Exit status 0