OK, this was a quite shitty implementation of a hard coded expiration date on a free license.. 
Step by step how to fix the problem by updating to latest version (Linux Ubuntu/Debian, you need to replace with your current username and foldername):
1. Shutdown the server
Code:
cd /home/teamspeak/teamspeak3-server_linux_amd64
Code:
./ts3server_startscript.sh stop
2. Make a backup of the entire folder
Code:
cd /home/teamspeak/
Code:
cp teamspeak3-server_linux_amd64 teamspeak3-server_linux_amd64_BACKUP
3. Download the latest version (3.3.1)
Code:
wget http://dl.4players.de/ts/releases/3.3.1/teamspeak3-server_linux_amd64-3.3.1.tar.bz2
4. Unpack over your current folder (it must be named teamspeak3-server_linux_amd64)
Code:
tar -xvf teamspeak3-server_linux_amd64-3.3.1.tar.bz2
5. Start the server again, your existing structure and permissions should remain
Code:
./ts3server_startscript.sh start
That's it.