Positron emission tomography is one of the most mature techniques for monitoring the particles range in hadron therapy, aiming to reduce treatment uncertainties and therefore the extent of safety margins in the treatment plan. In-beam PET monitoring has been already performed using inter-spill and post-irradiation data, i.e. while the particle beam is off or paused. The full beam acquisition procedure is commonly discarded because the particle spills abruptly increase the random coincidence rates and therefore the image noise. This is because random coincidences cannot be separated by annihilation photons originating from radioactive decays and cannot be corrected with standard random coincidence techniques due to the time correlation of the beam-induced background with the ion beam microstructure. The aim of this paper is to provide a new method to recover in-spill data to improve the images obtained with full-beam PET acquisitions. This is done by estimating the temporal microstructure of the beam and thus selecting input PET events that are less likely to be random ones. The PET detector we used was the one developed within the INSIDE project and tested at the CNAO synchrotron-based facility. The data were taken on a PMMA phantom irradiated with 72 MeV proton pencil beams. The obtained results confirm the possibility of improving the acquired PET data without any external signal coming from the synchrotron or ad hoc detectors.