Thanks for the log file.
VPS Debian x86_64 OpenVz
Is this system hosted by OVH? I just know that they have many issues with their network - especially with their OpenVZ VPS server.
Hosting has written that he has provided a firewall
Ok, this firewall may detects your clients connections as flood/DDoS/DoS and this could be one reason why they all loose their connection at the same time. A firewall can block the connections from their IPs for a while.
Are you still able to connect to your server via SSH or something else at this time? You should ask your hosting provider for further details about the firewall.
Another reason also could be, if the connections from the same IP is limited. For example in the same house are living a family with two kids, which are both on your TeamSpeak 3 server. With a Anti-DoS rule, you are able to block this traffic to prevent more connections from the same IP. TeamSpeak ATHP (= Hoster) are may using this feature, because it is a nice feature inside the server software. But it is also possible with every another firewall solution to rule those connections.
If you "telnet" your server, you can view this setting by sending the following ServerQuery command:
Zitat[...]serverinstance_pending_connections_per_ip=0
error id=0 msg=ok
Hint: You need to be logged in.