At this time we don't offer a persistent URL through the web portal. It's a commonly requested feature. The links also need to be refreshed after 30 minutes of connection time for a free account. Ths goes to 2 hours with a builder account or 8 hours for a commercial account.
Ways around this:
1) Use the APIs at http://docs.weaved.com within your own program to refer to your services by name, then request a proxy connection when you need it.
2) Use the peer to peer connection as described for ssh: http://forum.weaved.com/t/updated-script-for-fast-ssh-connections/623/ this is most straightforward on Mac or Linux but can be accomplished on Windows as well.
Please let me know your OS and what type of connection you're making: ssh, http, vnc, etc.