General questions on the CMA equalizer
In general equalizing a channel with deep fades is a problem for all equalizers. CMA equalizer is no exception. Absence of a training signal makes things worse.
This is obviously an example of the CMA stuck in a local minimum. The inital condition of the CMA equalizer was probably in the vicinity of the local minimum. The equalizer filter to which the CMA converged, convolved with the channel does not yield to an impulse-like overall response.
Remember that the cost functions of CMA equalizers are nonlinear. Modifying the modulus do not have a "linear" effect on the cost function. What happened probably was that your initial condition (which is identical to the one in the previous case) of the "modified modulus" CMA equalizer had now fallen into the vicinity of the global minimum. This is the "beauty" of nonlinearity!