An accelerator-based boron neutron capture therapy (BNCT) system that employs a solid-state Li target can achieve sufficient neutron flux derived from the 7Li(p,n) reaction. However, neutron production is complicated by the large thermal load expected on the target. The relationship between neutron production and thermal load was examined under various conditions. A target structure for neutron production consists of a Li target and a target basement. Four proton beam profiles were examined to vary the local thermal load on the target structure while maintaining a constant total thermal load. The efficiency of neutron production was evaluated with respect to the total number of protons delivered to the target structure. The target structure was also evaluated by observing its surface after certain numbers of protons were delivered. The yield of the sputtering effect was calculated via a Monte Carlo simulation to investigate whether it caused complications in neutron production. The efficiency of neutron production and the amount of damage done depended on the proton profile. A more focused proton profile resulted in greater damage. The efficiency decreased as the total number of protons delivered to the target structure increased, and the rate of decrease depended on the proton profile. The sputtering effect was not sufficiently large to be a main factor in the reduction in neutron production. The proton beam profile on the target structure was found to be important to the stable operation of the system with a solid-state Li target. The main factor in the rate of reduction in neutron production was found to be the local thermal load induced by proton irradiation of the target.