We've resolved this problem. If you are on Windows it is the Windows firewall that is blocking Java 7 when it sees certain FTP commands being sent (PASV and PORT).
Normally, the Windows firewall prompts to add a newly installed program. But in this case it doesn't seem to happen - we aren't sure why.
To resolve the problem, go to Windows Firewall Settings, and in the Exceptions tab, choose "Add Program" to add java.exe by browsing to your installation of Java 7.