Streaming recurrent models enable efficient 3D reconstruction by maintaining persistent state representations. However, they suffer from catastrophic forgetting over long sequences due to balancing historical information with new observations. Recent methods alleviate this by deriving adaptive signals from the attention perspective, but they operate on single dimensions without considering temporal and spatial consistency. To this end, we propose a training-free framework termed TTSA3R that leverages both temporal state evolution and spatial observation quality for adaptive state updates in 3D reconstruction. In particular, we devise a Temporal Adaptive Update Module that regulates update magnitude by analyzing temporal state evolution patterns. Then, a Spatial Context Update Module is introduced to localize spatial regions that require updates through observation-state alignment and observation changes. These complementary signals are finally fused to determine the state updating strategies. Extensive experiments show that TTSA3R achieves competitive performance on standard short-sequence benchmarks and provides substantially stronger robustness on extended sequences. On NRGBD, as sequences extend from 50 to 250 frames, TTSA3R exhibits only a 1.33$\times$ error increase, compared with 3.8$\times$ degradation for CUT3R. This highlights the practical value of temporal-spatial adaptive updates for long-term reconstruction stability. Our code is available at \url{https://github.com/anonus2357/ttsa3r}.

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