You probably saved those videos some time ago, before updating your game to version 1.1 or 1.2. The problem is that, after updating your game to one of those versions, you are not able to watch your old videos anymore. It is mentionned in the patch notes for both of those updates:
Battle Videos recorded before this patch can no longer be viewed
The only way to see those videos again would be to get back to the version of the game when you did the corresponding battles. You should then probably try to record them with some external sources so you can watch those later again, before updating back to the current version.
Some users performed it on Reddit, and apparently it worked well for them:
I was wondering if it was safe too so I deleted the update I had on Moon. Sun's my main and it has a lot of stuff on it while Moon is a new save file so I had less to risk with it.
Not only is it perfectly safe to remove the update data, after doing it I was also able to access the old Battle Videos afterwards as well.