My wife had trouble figuring out how to loop video on an iPhone. There's a lot of misinformation out there. Many people say you need a separate app to do this.
We managed to get this functionality from iOS 7 for free.
Go to Settings.
Go to Photos & Camera.
Scroll down to "SLIDESHOW". Turn on "Repeat".
Create a new album, put the video(s) you want to loop into it.
When you want to play it, select the album.
Select the video.
At the bottom of the screen is the little "box with an upward arrow" icon.
Press that icon.
You get a screen that allows you to select "Slideshow". Press "Slideshow".
You get a screen that allows you to select iPhone or AirPlay. Make your selection.
Press "Start Slideshow"
It loops.
Hope this helps.