Thanks for the responses.
My application is a 2.5in wide kevlar/aramid cogbelt, 8mm tooth pitch, on a secondary drive shaft between a 150HP reciprocating engine and the main rotor shaft on an experimental class helicopter. The cog belt pinion sprocket is 3.5in diameter and it drives a 14in main sprocket.
The small sprocket is on a 30mm shaft, overhung by about 2.25in, alloy unknown, Rockwell C hardness 0f 34. Main shaft turns at 520RPM, secondary shaft turns at 2080RPM. Dimension between the main rotor shaft and secondary shaft is about 20in.
This secondary shaft snapped just below the small cog sprocket and just inside the bearing race, at 155 hours operation.
Break appears to be from bending fatigue. Cog belt tension has been maintained loose enough not to assert undue side load on the shaft, but tight enough so that belt teeth don't climb sprocket teeth.
I suspect that belt oscillation is inducing cyclical side load on the secondary shaft at some frequency, eventually resulting in fatique and failure, but need to discuss this with an expert.