After reading the manual for the 6 fire i can see that it supports multi-client, multi-channel and multi driver type streaming from both windows audio and a client DAW.
I can't see really why you should be having this problem.
Can you tell us the following please?
1. What EXACT operating system you are running i.e 'Windows XP Home SP1'
2. What version of Reason you are running
3. What your PC spec is including MOBO, GFX, RAM and CPU types and amounts
Perhaps you could include some screenshots.
Have you tried different DAW programs to try and replicate the problem.
As a short term solution perhaps you could run your OS sound playback from your onboard s/c on your MOBO and run an analog line to the input of your terratec. You wont lose quality really, and for playback of web audio it makes not the slightest difference.
Regards!