The structural characterization of polymers and, in particular, of those used in Additive Manufacturing (AM) technologies, is essential to improve the understanding of their structure-property relationship for promising high-performance applications. For this, (scanning) transmission electron microscopy-electron energy loss spectroscopy, (S)TEM-EELS is an outstanding tool for exploring materials chemical and structural characteristics at high spatial resolution. However, the high beam-sensitivity of soft materials, such as polymers, hinders the possibility of probing in-depth analysis provided by (S)TEM-EELS. In this work, we analyse the electron beam irradiation damage of four polymers commonly used in Fused Filament Fabrication (FFF), namely polylactic acid (PLA), polycaprolactone (PCL), acrylonitrile butadiene styrene (ABS) and acrylonitrile styrene acrylate (ASA). For this, sequential low-loss and core-loss EEL spectra have been recorded, and the related signals have been monitored as a function of the accumulated dose. Our results show that the critical electron doses using the specimen thickness variations are larger for polymers containing aromatic groups (ABS and ASA) than for aliphatic polymers (PLA and PCL). Regarding the different elements, a larger sensitivity to the electron beam of oxygen regarding carbon and nitrogen is also evidenced. Our results have shown that polymer degradation occurs to a larger extent in the initial steps of electron irradiation, for very low accumulated electron doses, meaning that care should be taken in the selection of the microscopy settings to avoid artefacts produced by the electron beam. Degradation pathways for the four polymers studied are discussed.