I don't know when Apple fixed this problem but iCloud My Photo Stream has been working now for me for almost a month.
When I originally posted back in December of 2013 it would stop working after a day or two.
What worked for me was pretty easy.
If there are any photos in your My Photo Stream folder on the PC that you haven't already saved anywhere then Open the folder and safe the files somewhere on your PC. The procedure below will sync your PC to iCloud and any old photos in My Photo Stream will be deleted when the PC, iCloud and all of your iOS connected devices are sync'd.
For a PC.
1. Open iCloud Control Panel
2. Click the Sign out tab in the lower left corner.
3. Click Keep copy
4. If Outlook is open then save your work and allow Close Outlook and continue.
5. You will get a message that iCloud stuff is saved in Outlook and iCloud Photos are turned off.
6. Sign back into iCloud with your Apple ID.
7. Check the boxes to select the items you want to sync to your PC with iCloud and click Apply
8. Click Merge to merge bookmarks with iClould (if you checked that box).
It will download items from iCloud and tell you Setup is complete.Click Done and Close.
It will take some time to down load all your photos to My Photo Stream on the PC as well as any shared streams you may have.
iCloud only keeps photo stream photos in iCloud for 30 days, even though your last 1000 photo will remain on your device until deleted. Updating the iOS deletes everything from the phone; reconnecting to photo stream redownloads photos from the last 30 days (as older ones are no longer in iCloud).
To keep your photos permanently, import them to your computer while they are still in your camera roll (or save them to your camera roll from your photo stream album), as explained here:http://support.apple.com/kb/HT4083.
I found that iCloud Photos in shared photo streams remained even though they were much older than 30 days.
My Photos does not sync videos by design. It sounds like iOS 8 will enhance iCloud photo sharing but I don't know if it will include video syncing.