Check if the disk is full. Use a ssh client and log on to your ATV. User is "root" and password is "alpine". The ip you can find in the network section of settings on ATV.
After logon, run the command: "df -h /private/var" (do not include the ")
It should reply something like this:
Filesystem Size Used Avail Use% Mounted on
/dev/disk0s1s2 6.8G 1.8G 5.0G 27% /private/var
Only 27% is used, and there are 5Gigabytes available.
What I've seen is that the directory for movies doesn't clear whan movie is seen.
If there is less than 2Gb available, erase this cache manualy with command:
"rm -rf /private/var/mobile/Library/Caches/AppleTV/Video/LocalAndRental/*"
Then ATV will buffer OK again.