Liquid scintillating phantoms have been proposed as a means to perform real-time 3D dosimetry for proton therapy treatment plan verification. We have studied what effect radiation damage to the scintillator will have upon this application. We have performed measurements of the degradation of the light yield and optical attenuation length of liquid scintillator and water-based liquid scintillator after irradiation by 201 MeV proton beams that deposited doses of approximately 52 Gy, 300 Gy, and 800 Gy in the scintillator. Liquid scintillator and water-based liquid scintillator (composed of $5\%$ scintillating phase) exhibit light yield reductions of $1.74 \pm 0.55 \%$ and $1.31 \pm 0.59 \%$ after $\approx$ 800 Gy of proton dose, respectively. Whilst some increased optical attenuation was observed in the irradiated samples, the measured reduction to the light yield is also due to damage to the scintillation light production. Based on our results and conservative estimates of the expected dose in a clinical context, a scintillating phantom used for proton therapy treatment plan verification would exhibit a systematic light yield reduction of approximately $0.1\%$ after a year of operation.