The internal gravity modes of the Sun are notoriously difficult to detect, and the claimed detection of gravity modes presented by Fossat et al. ( Astron. Astrophys. 604, A40, 2017) is thus very exciting. Given the importance of these modes for understanding solar structure and dynamics, the results must be robust. While Fossat et al. described their method and parameter choices in detail, the sensitivity of their results to several parameters was not presented. Therefore, we test the sensitivity of the results to a selection of the parameters. The most concerning result is that the detection vanishes when we adjust the start time of the 16.5-year velocity time-series by a few hours. We conclude that this reported detection of gravity modes is extremely fragile and should be treated with utmost caution.