As imaging systems become more advanced and acquire data at faster rates, increasingly dynamic samples can be imaged without concern of motion artifacts. For optical interferometric techniques such as optical coherence tomography, it often follows that initially, only amplitude-based data are utilized due to unstable or unreliable phase measurements. As systems progress, stable phase maps can also be acquired, enabling more advanced, phase-dependent post-processing techniques. Here we report an investigation of the stability requirements for a class of phase-dependent post-processing techniques - numerical defocus and aberration correction with further extensions to techniques such as Doppler, phase-variance, and optical coherence elastography. Mathematical analyses and numerical simulations over a variety of instabilities are supported by experimental investigations.