I've followed the shooting star to its landing point, the Shining Casing appears in the world, but when I walk over to pick it up, it starts to travel toward me, but I hear a glass-breaking noise and nothing is receive in inventory. Other items dropped during the impact are picked up just fine.

Also, not sure if this is related, but I cannot find the Shining Casing in JEI.

Forge Version: 2768
AS version: 1.10.3

Casing shouldn't show in JEI. Also, you are 7 releases behind, and in a release version where your knowledge will be wiped every time you restart the pack, so chasing the casings doesn't really matter right there. Please update to at least 1.10.4.

If it breaks when you pick it up, it's not flagged for your player ID. You can only pick up casings for your own Stars. If it has somebody else's ID attached to it, (like if you're basing with somebody else, or they are near you), you're not going to be able to get it.