You may need to use Firefox portable on a machine already running another instance of Firefox (may be the one regularly installed on that machine). Firefox allow multiple instance (eventually with different profiles) using the command line parameter -no-remote.
This option is not available on Firefox portable.
To enable a second instance of Firefox portable, just open the portable folder of Firefox, enter the Other folder and inside it the Source folder. There you’ll find a FirefoxPortable.ini file. Copy it on the main portable folder (where there is the FirefoxPortable.exe file) and open it with a text editor.
Find the line “AllowMultipleInstances” and change it’s value from false to true. It should work!