This letter validates adaptive event-triggered stabilization confronting the coupling of estimate signal and system states for nonlinear systems with intractable large uncertainties. Notably, in the context, the evaluation on the changing rate of relative error is hampered while unavoidable for inter-execution time analysis. By taking advantage of the structure feature of controller function, that is not exploited in previous works, a convergence-preserving adaptive event-triggering mechanism is proposed in this letter. The relative/absolute thresholds are delicately online adjusted to maintain the effectiveness of the adaptive mechanism, while explicit pre-evaluation is provided for the minimum inter-execution time. The new event-triggered scheme enables double-side communication reduction, unlike those in related works only matching one-side event-triggered execution since continuous sensor-to-controller communication is required for certain event real-time directly evaluating the controller signal.