Basically although it's mutable composition, apple recommend to create an immutable composition and create AVPlayerItem for playback purposes. It's a bit annoying but you can go around it. When you want to refresh the video just sample the time, create another AVPlayerItem and load it to the right time.
Here's snippet from apple's AVMutableComposition documentation
AVMutableComposition is a mutable subclass of AVComposition you use
when you want to create a new composition from existing assets. You
can add and remove tracks, and you can add, remove, and scale time
ranges.
You can make an immutable snapshot of a mutable composition for
playback or inspection as follows:
AVMutableComposition *myMutableComposition =
<#a mutable composition you want to inspect or play in its current state#>;
AVComposition *immutableSnapshotOfMyComposition = [myMutableComposition copy];
// Create a player to inspect and play the composition.
AVPlayerItem *playerItemForSnapshottedComposition =
[[AVPlayerItem alloc] initWithAsset:immutableSnapshotOfMyComposition];
Further information: Full Document