The stability of polycyclic aromatic hydrocarbons (PAHs) upon soft X-ray absorption is of crucial relevance for PAH survival in X-ray dominated regions (XDRs). PAH stability depends on molecular size but also on the degree of hydrogenation that is related to H2 formation in the interstellar medium (ISM). In this project, we intend to reveal the changes of electronic structure caused by hydrogenation and the impact of hydrogenation on the stability of the carbon backbone for cationic pyrene and its hydrogenated derivatives by analysis of near C K-edge soft X-ray photoions. In our experiments, the PAH cations were trapped in a cryogenic radiofrequency (RF) linear ion trap and exposed to monochromatic X-rays with energies from 279 eV to 300 eV. The photo-products were mass-analyzed by means of time-of-flight (TOF) spectroscopy. Partial ion yields (PIYs) were then studied as a function of photon energy. X-ray absorption spectra computed by time-dependent density functional theory (TD-DFT) aided the interpretation of the experimental results. A very good agreement between experimental data and TDDFT with short-range corrected (SRC) functionals for all PAH ions was reached. The near-edge X-ray absorption mass spectra (NEXAMS) exhibit clear peaks due to C 1s transitions to singly occupied molecular orbitals SOMO and to low-lying unoccupied molecular orbitals. In contrast to coronene cations, where hydrogen attachment drastically increases photostability of coronene, the influence of hydrogenation on photostability is substantially weaker for pyrene cations. Here, hydrogen attachment even destabilizes the molecular structure. An astrophysical model describes the half-life of PAH ions in interstellar environments.