Gamma-ray bursts (GRBs) are the most powerful transient objects in the Universe, and they are a primary target for the MAGIC Collaboration. Recognizing the challenges of observing these elusive objects with Imaging Atmospheric Cherenkov Telescopes (IACTs), we implemented a dedicated observational strategy that included an automated procedure for rapid re-pointing to transient sources. Since 2013, this automated procedure has enabled MAGIC to observe GRBs at a rate of approximately ten per year, which led to the successful detection of two GRBs at very high energies (VHE; E > 100 GeV). We present a comprehensive analysis of 42 non-detected GRBs (4 short GRBs) observed by MAGIC from 2013 to 2019. We derived upper limits (ULs) on the observed energy flux as well as on the intrinsic energy flux corrected for absorption by the extragalactic background light (EBL) from the MAGIC observations in selected energy and time intervals. We conducted a comprehensive study of their properties to investigate the reasons for these non-detections, including the possible peculiar properties of TeV-detected GRBs. We find that strong EBL absorption significantly hinders TeV detection for the majority of GRBs in our sample. For a subset of 6 GRBs with redshift z < 2, we compared the UL on the intrinsic flux in the VHE domain with the simultaneous X-ray flux, which is observed to be at the same level in the current population of TeV-detected GRBs. Based on these inferred MAGIC ULs, we conclude that a VHE component with a luminosity comparable to the simultaneously observed X-ray luminosity cannot be ruled out for this sample.
