The stability of the molecular self-assembled monolayers (SAMs) is of vital importance to the performance of the molecular electronics and their integration to the future electronics devices. Here we study the effect of electron irradiation-induced cross-linking on the stability of self-assembled monolayer of aromatic 5,5'-bis(mercaptomethyl)-2,2'-bipyridine [BPD; HS-CH2-(C5H3N)2-CH2-SH] on Au (111) single crystal surface. As a refence, we also study the properties of SAMs of electron saturated 1-dodecanethiol [C12; CH3-(CH2)11-SH] molecules. The stability of the considered SAMs before and after electron-irradiation is studied using low energy Ar+ cluster depth profiling monitored by recording the X-ray photoelectron spectroscopy (XPS) core level spectra and the UV-photoelectron spectroscopy (UPS) in the valance band range. The results indicate a stronger mechanical stability of BPD SAMs than the C12 SAMs. The stability of BPD SAMs enhances further after electron irradiation due to intermolecular cross-linking, whereas the electron irradiation results in deterioration of C12 molecules due to the saturated nature of the molecules. The depth profiling time of the cross-linked BPD SAM is more than 4 and 8 times longer than the profiling time obtained for pristine and BPD and C12 SAMs, respectively. The UPS results are supported by density functional theory calculations, which show qualitative agreement with the experiment and enable us to interpret the features in the XPS spectra during the etching process for structural characterization. The obtained results offer helpful options to estimate the structural stability of SAMs which is a key factor for the fabrication of molecular devices.