Offline-to-online reinforcement learning reduces interaction cost for real-world robot learning but suffers from persistent value estimation instability. Existing methods address this through pessimistic regularization, lower-bound calibration, and architectural normalization, but an overlooked source of instability lies in the entropy formulation: the standard log-entropy term can become negative, destabilizing policy updates. We introduce SCQ (Sigmoid-Bounded Conservative Q-Learning), which replaces this term with a sigmoid-bounded formulation that stays strictly positive. SCQ retains conservative Q regularization and return-based lower-bound calibration, stabilizing policy optimization without sacrificing exploration. We evaluate SCQ on D4RL (Minari) benchmarks under both single-demonstration and standard dataset settings, as well as on simulation and real-world visual tasks. SCQ matches or exceeds baseline performance while exhibiting more stable training dynamics across state-based and visual benchmarks, and transfers to four real-robot platforms including manipulation, wheeled, quadruped, and humanoid systems. A direct clipping intervention that removes negative log-probability contributions, together with gradient-matched positive-score controls, indicates that positivity rather than a particular score shape alone drives much of the improvement. Project website: https://scq-rl.github.io.

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