Here is what I understand about the general principles of fiber optics. I am no expert on the engineering aspect of them or properties of specific commercially available products.
We're talking wave-guides here and for the higher order modes the effective angle at which the plane waves (or photons if you wish) impinge upon the fiber walls is greater. (until you have 90deg to the wall for standing waves). Thus higher modes will be reflected less and escape more readily when the fiber bends. Whether you are modeling fibers as internally reflecting or whether there is axially focusing refraction due to radial difference in index of refraction this should be the same issue with higher modes. Above some order, the fiber just can't retain that mode of the light at that frequency. How high a mode order can be sustained would be a function of the fiber's material properties and diameter and I imagine that need not exclude several of the lowest order modes in some cases.