I had extract same failure and did lean a lot about BMW all wheel drive. This seams to be odd failure and not much experience on forum. I did post some learning in Bimmerfeast “ question about Transfer case” I do not know what let the axles pop out I just replaced my differential with one from junk yard. Did not want to chance it doing it again. Side note my power train is much quieter and smoother with replacement Diff. I did not realize it was getting louder!

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Astrok
2005 X5 4.8IS
2008 X5 4.8
2005 X3 3.0
2006 MB R500
2001 Slk 232