Why do Bohr diagrams not work for elements after calcium? More specifically the Noble Gases Krypton and down.

They do work, but you need more knowledge of the atom past "8 electrons in a shell". This is because the 4s orbitals have a lower energy than the 3d orbitals, despite being in a different ring.

If you use your "8 electrons in a shell" model, then the noble gases will not have full outer shells, which they are supposed to have because that's why they are unreactive.

If you need any more explanation about 4s and 3d then please ask, but I believe they are beyond your level and that's why the bohr diagram doesn't work for you at this stage.