Following the Large Hadron Collider upgrade phase from 2019-2020, the innermost station of the ATLAS Muon Spectrometer is being replaced with a newly enhanced detector system. The new associated electronic system will provide improved precision tracking and triggering for the expected high background rates. In this system, the Read-Out Controller (ROC) ASIC is an essential on-detector custom real-time data packet processor. It buffers, filters and aggregates the digitized data from up to 512 upgraded muon detectors and distributes phase-adjustable clock signals and control commands. It is fundamental to verify the robustness of ROC and its data integrity despite the neutron dose at which it is expected to be exposed. This paper briefly describes the ROC architecture, data formats, die layout and implemented techniques for the mitigation of radiation effects. The ROC test apparatus and irradiation testing are thoroughly presented, giving emphasis to the immunity to the produced single event upsets (SEUs) and the effects of data corruption inside its SRAM. Two ROC samples were subjected to neutron beams with 20, 22 and 24 MeV energies, for over 39 hours, at an average flux of 9.5 × 105 n⋅cm−2⋅s−1, totaling a dose equivalent to 8 months of operation in LHC at L = 1034 cm−2⋅s−1. Flip-Flops were affected by 69 SEUs yet the ROC operation was not disturbed by this, but data corruption in memories occurred with a considerable rate. Statistics of the resulting errors are presented.