Due to the complex operating conditions and the high-temperature, high-pressure environment, the rotating detonation combustor (RDC) used in propulsion systems may experience partial failures of the fuel injectors, which in turn can degrade the RDC's operational stability. To address this issue, experiments were conducted to study the performance of RDCs under non-uniform injection conditions. The critical initiation detonation range and the propagation behavior of rotating detonation waves (RDWs) were explored under different non-uniform injection configurations. As the degree of injector non-uniformity increased, the critical initiation detonation range narrowed, and unstable propagation and low-frequency instabilities of RDWs were observed near the upper and lower limits. Frequency-domain analysis and signal peak analysis were employed to statistically characterize RDW propagation stability parameters. A typical range of injection parameters was proposed to guide the design of RDC injectors. The propagation mechanisms of RDWs within injection and non-injection regions during non-uniform injection were discussed in detail. It was found that increased fuel non-uniformity led to greater expansion losses of the leading shock wave in non-injection regions and reduced energy accumulation during combustion in injection regions. These combined effects degraded RDW propagation stability and could even cause detonation wave quenching. This study contributes to the reliable design of RDC injectors and provides insight into RDW propagation processes in non-uniform conditions.