This simply means that the client (DBD::Sybase, in this case) can't connect within the required time frame (60 seconds by default). This can happen when a firewall has been set up that simply drops packets instead of actively rejecting them (in the latter case you'd get a "connection refused" message instead).

So check the network to make sure that access is possible - you can try with "telnet <hostname> <port>" just to see if connectivity is available.

Michael