Composite polymer electrolytes (CPEs) for lithium-ion batteries provide an effective balance of ionic conductivity, mechanical robustness, and safety. Loss of charge capacity, however, is caused by several contributing factors. In this work we specifically examine mechanical changes in the composite electrolyte layer. We apply cyclic compression to mimic stress cycling that is caused by asymmetric volume changes during charging cycles between anode and cathode. Using a representative composite electrolyte formulation consisting of Li6.4La3Zr1.4Ta0.6O12 (LLZTO) at 10 wt. % in polyethylene oxide (PEO) with bis(trifluoromethane) sulfonimide (LiTFSI), we experimentally measure stress-strain characteristics, stress relaxation time, and cyclic compression of a composite electrolyte. We also examine the effect of particle size, by comparing 500 nm vs. 5 µm sizes. At 15% compressive strain, the addition of 500 nm particles increased strain energy density (SED) by a factor of 2.6 and the addition of 5 µm particles increased SED by a factor of 2.9. Both particle sizes showed similar relaxation time constant, but the 5 µm particles showed tighter repeatability than the 500 nm case. Both compositions exhibited continual decline in peak stress beyond 500 cycles of compression at 15% strain. These experiments reveal insights into how cyclic loading can alter the mechanical response of a composite electrolyte, and thereby contribute to the broader understanding of electrochemical and mechanical coupling in lithium-ion batteries.