Sampled Gabor phase retrieval --- the problem of recovering a square-integrable signal from the magnitude of its Gabor transform sampled on a lattice --- is a fundamental problem in signal processing, with important applications in areas such as imaging and audio processing. Recently, a classification of square-integrable signals which are not phase retrievable from Gabor measurements on parallel lines has been presented. This classification was used to exhibit a family of counterexamples to uniqueness in sampled Gabor phase retrieval. Here, we show that the set of counterexamples to uniqueness in sampled Gabor phase retrieval is dense in L^2(R), but is not equal to the whole of L^2(R) in general. Overall, our work contributes to a better understanding of the fundamental limits of sampled Gabor phase retrieval.