90.189.192.213:25565 (GS4 udp query port: 25566), firewall is allow traffic to specific ports. What's the matter?
(P.S. Periodically site shows server online, but after some scan shows offline again)

You'll need to determine which of the following IPs are getting blocked:

208.167.241.190
208.167.241.185
208.167.241.186
108.61.78.147
108.61.78.148
108.61.78.149
108.61.78.150

I enable debug mode in server.properties and i got this info:

[INFO] Packet len 7 [/208.167.241.186:52624]
[INFO] Packet '09' [/208.167.241.186:52624]
[INFO] Challenge [/208.167.241.186:52624]
[INFO] Packet len 15 [/208.167.241.186:52624]
[INFO] Packet '00' [/208.167.241.186:52624]
[INFO] Rules [/208.167.241.186:52624]
[INFO] Challenge [/208.167.241.186:52624]

But site says me: Could not scan server.
Then, I pressed button "update scanning parameters" 3 times and on the last press i got message "Status updated". Log in this time are the same entries. This may mean that the response UDP packets are lost?

Glad to hear that it started scanning. If it goes offline quickly after that, again, you'll need to determine which of the mentioned IPs you have blocked.

Nothing blocked.
Iptables default INPUT filter - ACCEPT. And no block anything rules.
Last scan's (after my previous message) made from this address: 108.61.78.149 and no others.

I just sent a couple test scans and it doesn't seem that your server is using the proper query protocol.

I would recommend the following:

1. Ensure your server is up to date.
2. Remove any query plugins (minequery) and plugins that you think may possible be an issue (note: if you use MCPC+ it messes up the query protocol)

Then monitor it again.

Hmm, I do nothing, but site shows the server alive.