Hi Andreas,
please have a look at this WIKI which shows examples on how to troubleshoot SQLA connections.
https://wiki.scn.sap.com/wiki/display/SQLANY/How+to+Troubleshoot+Connections+to+SQL+Anywhere+Server
Ideally, you would like to start a SQLA server on a default (2638) or different port:
e.g.
dbsrv17 -n demo17 -x tcpip(port=5000) -z -o console.log demo17.db
make sure you can connect from the same machine using tcpip
e.g.
dbping -d -c "LOG=conn.log;uid=dba;pwd=sql;eng=demo17;LINKS=tcpip(host=localhost;port=5000);dbn=demo17"
then go to your remote machine and try the same ( just change "HOST=<remote>" )
e.g. dbping -d -c "LOG=conn_remote.log;uid=dba;pwd=sql;eng=demo17;links=tcpip(host=<remote_host|IP>;port=5000);dbn=demo17"
If you can connect locally but not remotely , just like Jason said, most likely it's a firewall.
To veryfy if tcp port is open, the easiest would be to try with telnet :
telnet <IP> <port>
(if the port is closed , you'll see a timeout error).
Lucjan