Low-Gain Avalanche Detectors (LGADs) are a type of thin silicon detector with a highly doped gain layer that provides moderate internal signal amplification. One recent challenge in the use of LGADs, studied by several research groups, is the gain suppression mechanism for large localized charge deposits. Using the CENPA Tandem accelerator at the University of Washington, the response of the LGADs to MeV-range energy deposits from a proton beam was studied. Two LGAD prototypes and a PIN diode were characterized, and the gain of the devices was determined as a function of bias voltage, incidence beam angle and proton energy. This study was conducted in the scope of the PIONEER experiment, an experiment proposed at the Paul Scherrer Institute to perform high-precision measurements of rare pion decays. A range of deposited charge from Minimum Ionizing Particle (MIP, few 10 s of KeV) from positrons to several MeV from the stopping pions/muons is expected in PIONEER; the detection and separation of close-by hits in such a wide dynamic range will be a main challenge of the experiment. To achieve this goal, the gain suppression mechanism has to be understood fully.