If you are experiencing problems with version 1.0 of reK ReplayKit Plugin for iOS running in Unity 5.3, here are some technical details and a quick fix while we re-submit a fixed package to the AssetStore for review.
The problem is that Unity 5.3 introduced some changes to how [ExecuteInEditMode] and DontDestroyOnLoad() works, which results in the destruction of the reK prefab instance whenever you open a test scene in the editor or drag the prefab into your own scene.
In order to fix this, just locate the Awake() call in UnityReplayKit.cs and change this
if (dontDestroyOnLoad == true) { DontDestroyOnLoad(gameObject); }
into
if (Application.isPlaying == true && dontDestroyOnLoad == true) { DontDestroyOnLoad(gameObject); }
and you are done.
The fix will ship with the next update of reK.