The well-known performance breakdown of subspace-based parameter estimation methods is usually attributed to a specific property of the technique, namely ``subspace swap''. In this paper, we derive the lower bound for the maximum likelihood ratio (LR), and use it as a simple data-based indicator to determine whether or not any set of estimates could be treated as a maximum likelihood (ML) set. We demonstrate that in those cases where the performance breakdown is subspace specific, this LR analysis provides reliable identification of whether or not ``subspace swap'' has actually occurred. We also demonstrate that by proper LR maximisation, we can extend the range of signal-to-noise ratio (SNR) values and/or number of data samples wherein accurate parameter estimates are produced. Yet, when the SNR and/or sample size falls below a certain limit for a given scenario, we show that ML estimation suffers from a discontinuity in the parameter estimates, a phenomenon that cannot be eliminated within the ML paradigm.