Finite Rate of Innovation (FRI) sampling theory has shown that it is possible to sample and perfectly reconstruct classes of non-bandlimited signals such as streams of Diracs. In the case of noisy measurements, FRI methods achieve the optimal performance given by the Cramér-Rao bound up to a certain PSNR and breaks down for smaller PSNRs. To the best of our knowledge, the precise anticipation of the breakdown event in FRI settings is still an open problem. In this letter, we address this issue by investigating the subspace swap event which has been broadly recognised as the reason for performance breakdown in SVD-based parameter estimation algorithms. We work out at which noise level the absence of subspace swap is guaranteed and this gives us an accurate prediction of the breakdown PSNR which we also relate to the sampling rate and the distance between adjacent Diracs. Simulation results validate the reliability of our analysis.