Which device is it? Is it the Linksys/Cisco? What is the model and version number? Is there a firmware update for the device? Have you tried mapping using the IP address? Have you tried the NTLMv2 fix? and or the Encryption level fix?
Well according to this Linksys by Cisco - NSLU2 Support there hasn't been a firmware update since 2005, so I doubt if that will be much help. So try this type secpol.msc in the start or run dialog box and navigate according to screen shot, change selections to Send LM & NTLM - use NTLMv2 session security if negotiated and the other two to No minimum, reboot and see if that helps.
I wouldn't think so, but it's possible. Go ahead, if you haven't already, disable the Windows7 built in firewall and temporarily uninstall any third party applications, like Internet Security Suites, that may have firewall type function, you can always reinstall them later. You said, that it worked for a while after the clean reinstall of Windows 7 and then just ceased to work. Which would lead me to believe that something was installed and or updated which caused this to happen. If you boot into safemode with networking, can you access the drive as before or does the problem persist, even in safemode with networking?
determine the ip address of the device by using one of your other machines that are able to connect without issue. Boot the Win7 machine into safemode with networking (provided that your network drivers load....wired or wireless, which may be an issue) see if you can ping the device by ip address and then attempt to ping the device by netbios name, if you are successful, attempt to look at the device by typing \\192.168.nnn.nnn into the run dialog box (hold down the windows logo key and strike the \\"r\\" key and see if you get an error regarding access rights or name not found etc. Safemode with networking should be able to load nominal drivers to support at least a wired connection, test by opening a browser.