The estimation of sinusoidal signals is a very well researched area, and it is well known that two signals can be resolved well for frequency separation below the Fourier resolution at high enough signal to noise ratio. However, in the case of many closely spaced sinusoids estimation is impaired for separations well above the Fourier resolution, and the dependence on signal to noise ratio is involved. The problem is analyzed by considering the Hessian of the log-likelihood function. When there is some direction in the parameter space, where the curvature of its deterministic part (i.e. the Fisher information matrix) is less than the curvature of its stochastic part, this is an indication of problems for correct estimation. An expression for the probability of this to occur is presented.