We study decentralized smooth nonconvex optimization with a lower-bounded average objective and independent local trust-region acceptance decisions. Successful local trials can increase the average objective, while rejection produces a zero accepted inverse block at a nonzero gradient tracker. Our main contribution is a convergence analysis that permits such genuine local rejections. The method combines gradient tracking, positive definite quadratic models, and adaptive radii proportional to tracker norms. Under uniform communication contraction and explicit accepted-operator stability conditions, we prove vanishing stationarity, consensus, and tracking residuals and stationary consensus accumulation points. Finite acceptance windows and a Schur decomposition give a best-iterate iteration bound quadratic in the inverse residual tolerance, including all-rejected rounds. We give explicit admissible ranges for the step size and residual weight, and an exact heterogeneous four-node quadratic family in which every node rejects infinitely many nonzero trials. Numerical experiments examine the rejection mechanism
and compare fixed-parameter behavior with independently tuned baselines. The tests show that the trust-region safeguard prevents divergence of model-based steps at a common parameter choice, but radius adaptation gives no general performance advantage.