Backfill mining serves as an effective method to mitigate mining-induced pressure, control strata movement, and reduce surface subsidence in underground coal extraction. This paper elaborates the operational mechanisms of backfill hydraulic support. Based on strata movement characteristics in backfill mining and 8 typical overburden load patterns, equilibrium equations for the roof beam of six-columns backfill hydraulic supports are established. To investigate the fatigue characteristics of the six-leg backfill hydraulic support base, mechanical theoretical models for both the complete support structure and the base were established. Strength analysis of the base was conducted using the finite element method, revealing stress concentration locations and corresponding stress values under critical operating conditions. Based on the strength analysis results, fatigue life, fatigue damage, safety factor, and fatigue sensitivity analyses of the base were conducted using the Fatigue Tool. The results indicate that the base exhibits multiple stress concentrations under torsional loading conditions. These stress-concentrated areas demonstrate shorter fatigue life, higher fatigue damage, and lower safety factors, making them particularly prone to fatigue failure. The research results provide theoretical references for enhancing the service life of backfill hydraulic supports, thereby mitigating rockburst risks in roof strata and improving backfill mining efficiency.