The adapter does not provide enough power for the FireStudio Mobile to work properly. You must use the external power supply.
The Thunderbolt to FireWire adapter can provide up to 7W of power to devices that are attached by FireWire. This will provide only enough power for the FireStudio Mobile's power light to come on and the audio interface may not function properly. This would affect audio playback, recording, and 48V ( Phantom power for microphones ) functions.
Note: If your issue can't be relieved after connecting the external power supply then perhaps you need to check the FireWire cable that connects the FireStudio Mobile to the Thunderbolt adapter's FireWire 800 port. The following article explains proper FireWire S800 to S400 connectivity: http://support.presonus.com/entries/21234478
Apple Thunderbolt Adapters: Frequently asked questions (FAQ)