Adobe Dreamweaver's remote connection setting, whether it's FTP, SSH, SFTP, etc., can be incredibly temperamental. If you're running other apps like messaging or torrents in the background, or basically anything sharing the network connection (this could even be an email attachment download or other passive activity), Dreamweaver can report "Unable to connect", "Connection refused", and/or a few other warning when trying to connect with your remote server. While it may be more efficient to be uploading and downloading ftp-style files (large in size, delicate transfer, whatever) without anything else hogging bandwidth, that doesn't mean you shouldn't be able to. I had previously been unable to use Dreamweaver to establish any kind of connection with a remote server while running Adium or bittorrent, or a few other programs that used specific ports (not ftp ports though, so it shouldn't have mattered). Anyways, the following tricks may get you up and running with a server connection that Dreamweaver says isn't responding, when programs like CyberDuck or even built-in ssh / ftp commands are getting through just fine.

1 - Basics
Under 'Manage Sites' - Edit a site and make the 'Remote Info' tab visible. If using FTP, check Use Passive FTP (or uncheck) and hit Test. Try the same with Use Secure FTP. Try the same with the firewall, and also try turning the firewall on, and under 'Firewall Settings' disabling 'Disconnect after __ Minutes Idle'. Also, change FTP Time Out to 0 seconds. Firewall port 21 (default ftp port) works fine for me here. You can try IPv6 for the heck of it, but the problem is most likely underlying this... Note, the firewall changes you make apply to Dreamweaver's preferences, not to the site you're currently editing (IOW, settings apply to all sites).

2 - Router Snags
Run a traceroute through your shell (terminal, type traceroute the.ip.address.or.server.name Any large delays? While the firewall setting should have stopped this, you may still be seeing a hiccup which DW is getting timed out at.

(This is not a likely solution either, but at this point you can close DW, trash your preferences (~/Library/Preferences/Adobe Dreamweaver CS3 Prefs), and reopen. Change the firewall settings to 0 second timeout, or disable the firewall, and try to connect. If it works, hurrah, you're done.)

If the delay is between you and the gateway or the gateway and your ISP (or whatever the next step may be in your case), this may be easily curable. Try swapping out the router for an alternate, if you have it, and test DW's connection. If it's working, you will need to take a look at your router's settings. You can go crazy and check what packets are actually being sent through what ports by DW, or you can compare the routers firewall settings or any kind of port forwarding / triggering, blocking it may be doing and make changes accordingly. I have had many occurrences of this problem behind 2Wire and dlink routers with Dreamweaver, but nearly none behind my linksy router. My work Linksys, I should note, is running HyperWRT + Tofu (Tofu required for StarCraft :) but I've had good luck with any linksys.

3 - Try wired vs wireless network connections (if you haven't already). Wireless are prone to packet loss.

4 - Are you on Windows? Temporarily disable any firewalls, ip filters, etc., that may be interferring (if you haven't already). You should know that any type of mainstream anti-virus like Norton, Symantec, Mcafee, etc., will most likely block DW. Download AVG or something like that instead and save the money.

5 - Connected to an Apple base station? Enable FTP Access through the Airport control panel.

Still no luck? Post a comment. I've had loads of experience with Dreamweaver hiccups.