Seismic fragility curves of mechanical structures are key quantities of interest for probabilistic risk assessment studies. They express the probability of failure of a mechanical structure conditional to a scalar value derived from the seismic signal, coined intensity measure. This work targets studies for which the observed information of the structure’s response is limited to binary outcomes —failure or success— under a given seismic excitation as input (e.g., experimental results). For these, the Bayesian learning framework allows efficient estimation of the parameters that predict the fragility curve. It avoids the generation of unrealistic fragility curves such as unit step functions which are common with classical methods. Nevertheless, challenges remain. The approach still has to account for (i) the influence of the prior that can skew estimates, which is critical to auditability in the nuclear industry; and (ii) the emergence of “degenerative scenarii”. The latter are related to the distribution of the experimental data and can lead to improper posterior distributions, further emphasizing the need for a carefully chosen prior. To address these challenges, we propose a three-step methodology. First, we introduce a novel and robust prior, constructed as a ‘constrained’-reference prior. It allows the construction of a prior which is both proper and objective. Its implementation can be carried out either through its theoretical formulation or via the consideration of the output of an optimized neural network. Second, we conduct a sequential planning of experiments strategy to optimize the allocation of data. The design we suggest is constructed on the basis of sensitivity indices to measure the influence of data on the posterior distribution. Finally, we assess the impact of the constrained prior on posterior estimates to ensure the robustness and auditability of the methodology. The proposed methodology is validated on a case study taken from the nuclear industry. Our results demonstrate its effectiveness in resolving issues related to degenerative samples and providing robust seismic fragility curve estimates with limited experimental data.