There are many reasons why the fiber can fall out of the kiln prematurely, that said, it's not that hard to put back in place.  Here's a step by step guide:
Place the kiln upside down on a bucket so that it sits flat and stable with the opening upwards.
Carefully put the fiber back in place. Remember to line up the cutouts in the fiber with the cage cutouts.
You may need to un-bend the little hooks at the bottom just enough to put the fiber back, then re-crimp them.  They should hold the fiber but not pierce it.
Once it is in place, you will need to either:
Spray the kiln with a rigidizer (50:50 sodium silicate and water applied in three LIGHT coats should do the trick) OR
Create “buttons” and wire the fiber to the cage.  If you google buttons for raku kiln, you will see many options and photos of ceramic buttons BUT (and here is the great part) you don’t need to make them out of ceramic,
IF you have some scrap ceramic fiber laying around, you can make very small rolls of ceramic fiber, and use them instead.  I've done this trick a few times on kilns here at the shop, and it works great!! I use an 18ga annealed wire, and the twists are on the outside of the kiln.  Bend them flat against the outer blanket, and make sure you don’t twist them so tight that the wire pulls through the blanket.
You can use both methods together for added resiliency.