Dissipative cognitive architectures maintain computation through continuous energy expenditure, where units that exhaust their energy are stochastically replaced with fresh random state. This creates a fundamental challenge: how can persistent, context-specific memory survive when all learnable state is periodically destroyed? Existing memory mechanisms -- including elastic weight consolidation, synaptic intelligence, and surprise-driven gating -- rely on gradient computation and are inapplicable to systems that do not perform it. We introduce Deep Memory (DM), a backpropagation-free persistent memory mechanism operating through a triple-loop consolidation cycle: (1) recording of expert-specific content centroids, (2) seeding of replaced units with stored representations, and (3) stabilization through continuous re-entry. Discrete expert routing via Mixture-of-Experts (MoE) gating is required, in the regimes tested, to prevent the centroid convergence that would render stored memories identical. We derive a Foster-Lyapunov drift bound for the full triple loop, showing that seeding rescales the turnover noise floor. Across
1,007 simulation runs over thirteen blocks: (i) removing stable context-expert binding removes specialization (
MI=1.10 vs.
0.001;
n=91); (ii) DM achieves
R=0.984 vs.
0.385 without memory (
n=16); (iii) continuous seeding reconstructs representations after interference (
Rrecon=0.978; one-shot fails;
n=30); (iv) the mechanism operates within a characterized
(K,p) envelope (
n=350); (v) recording
× seeding is the minimal critical dyad (
n=40); (vi) associative and reservoir baselines (Hopfield, ESN) are compared under matched turnover (
n=370). DM is thus a falsifiable, bounded mechanism for persistent memory in backpropagation-free cognitive systems, with functional parallels to hippocampal consolidation.