[en] Scenarios where gravitinos with GeV masses make up dark matter are known to be in tension with high reheating temperatures, as required by e.g. thermal leptogenesis. This tension comes from the longevity of the NLSPs, which can destroy the successful predictions of the standard primordial nucleosynthesis. However, a small violation of matter parity can open new decay channels for the NLSP, avoiding the BBN problems, while being compatible with experimental cosmic-ray constraints. In this paper, we propose a model where matter parity, which we assume to be embedded in the U(1)_B-L gauge symmetry, is broken dynamically in a hidden sector at low scales. This can naturally explain the smallness of the matter parity breaking in the visible sector. We discuss the dynamics of the corresponding pseudo Nambu-Goldstone modes of B-L breaking in the hidden sector, and we comment on typical cosmic-ray and collider signatures in our model. (orig.)