Ok, as an example, let's look at your video. The tag for that is reloadableVideo.
You currently have animations there for menuIndex="0" (Main Menu) and menuIndex="1". Your onMenuExit animation fades out your video, so when you enter the 3rd level (and exit the second level) the video fades out. Since you don't have an animation for menuIndex="2", the video remains faded out. You could of course add animations for menuIndex="2", menuIndex="3", etc., but since all the animations appear to be the same you could also consider removing the animations for menuIndex="1", and just remove the menuIndex="0" from the first set of animations. I also removed a number of animations that really don't do anything (like moving the video to the location it's already at).
<reloadableVideo imageType="screenshot" alpha="1" x="0" y="bottom" yOrigin="bottom" Width="1920" layer="2">
<onMenuExit>
<set duration=".01">
<animate type="alpha" to="0" algorithm="easeinquadratic"/>
</set>
</onMenuExit>
<onMenuEnter>
<set duration=".01">
<animate type="alpha" to="1" algorithm="easeinquadratic"/>
</set>
</onMenuEnter>
<onHighlightExit>
<set duration=".01">
<animate type="alpha" to="0" algorithm="easeinquadratic"/>
</set>
</onHighlightExit>
<onHighlightEnter>
<set duration=".01">
<animate type="alpha" to="1" algorithm="easeinquadratic"/>
</set>
</onHighlightEnter>
<onExit>
<set duration=".01">
<animate type="alpha" to="0" algorithm="easeinquadratic"/>
</set>
</onExit>
</reloadableVideo>
I also notice that the animation is rather short; I'd consider making it a bit longer for a smoother animation, but that's me.
Now for the menu: you need to create a menu set for each menu layer you want. Currently there's only 2 of them defined; you'll need to add menus for layer 3, etc. You can simply copy the one for menuIndex="1", and then replace all the menuIndex="1" with menuIndex="2". Continue as needed for the amount of menu levels you want.