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A barrel-shaped plastic scintillation counter with Multi-Pixel Photon Counter (MPPC) readout has been developed and operated in the first WASA-FRS experimental campaign at GSI. The detector was used to measure charged particles emitted from reactions induced by a 2.5 GeV proton beam incident on a carbon target, providing particle identification in combination with momentum reconstruction in a 1 T magnetic field. The performance of this detector, particularly its response to energy deposition and time resolution, was systematically investigated as a function of count rate and total number of irradiating protons. A time resolution of 45-75 ps (σ), depending on the energy deposition, was achieved. Stable performance was maintained under high-rate conditions up to 1.35 MHz per single counter, with no significant degradation in either signal amplitude or timing response. Radiation-induced damage to the MPPCs was observed primarily as a reduction in signal amplitude, with approximately 35% decrease at an estimated 1 MeV neutron-equivalent fluence of 2.4 x 10¹⁰ cm^-2.