I am a bit confused here. The right side on the scetch is the motor side, yet you indicated that the fracture is at the non-driven end. If it is at the non driven end, torsion can not be the cause. In that case test the resonance, just do a bump test, take an FFT with an accelerometer on the...
The right side is the side where the motor mounted. Have you considered torsional resonance as a cause. I will show you an example of a shaft from a centrifuge, due to torsional overload.
http://files.engineering.com/getfile.aspx?folder=092500fe-e8b1-463d-9e9d-237de42dce2c&file=SHaft_DSC03059.JPG