I have tested a local machine running Windows 2008 R2 Server and I have not been able find any problems, everything appears to work correctly in my tests.
Assuming FlashFXP is configured correctly to run the task regardless of whether the user is logged in or not then the task should run.. If its not running is there an error message?
Do you have logging enabled for the task? You might want to enable session logging to help troubleshoot the issue.
Also for reference what type of entries does the transfer queue contain, uploads, downloads, or site to site transfers?
If you've tried all that and you're still having problem can you please try the latest development build, you can download it
here