I had the same problem, and used part of SurfAfghanistan's answer.
1. Go To system
2. Go to Storage Device
3. Select Games and Apps (whereever your game saves are)
4. Scroll down to "Ns" and select Netflix
5. If you have two or more Netflix App files on your storage device, read the * section immediately below. If you only have one Netflix App file, skip to 6
*the key is to select the Netflix with the earliest date. I had two Netflix Apps, so had to check the dates on both. To check the date, simply press "A" over one Netflix App icon. In the next screen, you will see 3 files, "Saved Game", "Xbox 360 Save", and "Update". Select either one of these files. In the next screen, look in the bottom right hand side of the screen and see the date for that file you just selected. Keep this in mind. Go back to the front screen and select the other Netflix App Icon. Repeat the same process until you see a date. I had one file created 12/22/2011 and one created 7/24/2011. I deleted all files in the July folder after confirming the dates..exit back to saved files..and continue to #6*
6. Click the newest Netflix App file. In the next screen, select and delete the "Saved Game" file
7. Exit out of Storage
8. Reopen Netflix, log in.
This worked at 2039HRS EST on 22 December 2011 for me. Gamertag KREAM01.
Hope this helps.