I had a similar problem. It wouldn't let me back up to my windows partition mounted on /mnt/win_d (Z:\mnt\win_c). What I ended up doing is making a directory on C: (fake_windows) where I would do the backup and then manually copying it to the other partition. I suppose a more elegant way would be to change the desktop/menu item for Quicken to point to a shell script that would go something like this:
~/cxoffice/bin/wine --check --cx-app "C:////Program Files////Quicken////qw.exe"
cp -f ~/.cxoffice/dotwine/fake_windows/quicken_backup/* /mnt/win_d/quicken_backup
When I was using Windows, Quicken was also pretty picky about where it would back up to. One time my computer crashed. When I rebooted, I skipped the disk check, and when Quicken went to back up, it refused. I have a feeling that quicken tries to do some lower level file system checks before allowing a backup. If this is the case, then the problem we are having is in the way wine/cxo implements the drives other than C:. I should post this on the mailing list...
Hope that helps!