There could be a couple causes to this issue. The device could be out of space while recording video. Be sure to check "Available" under settings/general/about. If there is minimal space, then import all photos and videos to your computer then delete them from the device. The first article goes over how to process these steps. A restore as new might be needed if the issue persists. The second article goes over how to import all your data so it is not lost. The last article, covers how to restore and setup as new.
Hope this helps,