If you click on the "My FatSecret" link at the top left and then scroll way down, you'll see an area on the right hand side that says something like "Buddy Requests". If you accept from there rather than from email it usually works. You should see the buddy reqest disappear and your newly accepted buddy appear in your buddy list.
If that doesn't work, sign out of Fat Secret totally, clear your computer internet files and cookies, reboot your comluter, then sign back in and try again.
Hope this helps!