Long-running LLM agents require memory that persists and evolves across sessions. Text-based memory retrieves and reconstructs past interactions at every query, making long-horizon performance increasingly dependent on retrieval quality and contextual reasoning as histories grow. Parametric memory encodes experience directly into model computation, but existing approaches provide limited support for cross-session memory evolution. Their coupling to a specific backbone further restricts memory reuse after model replacement. We introduce RPMem, a two-stage architecture that compiles each session into a model-independent latent memory through forward computation and selectively integrates it with retained memory via a task-trained recurrent gate. The consolidated memory is then mapped to backbone-specific low-rank adaptation (LoRA) parameters, allowing the encoding capability to transfer when the backbone is replaced. Evaluation across three long-term memory benchmarks and five diverse backbones demonstrates broad generalization with near-constant update cost and memory footprint. With Qwen3-8B on PERMA, RPMem reaches 85.52%, outperforming the strongest parametric and text-based baselines by 5.32 and 12.98 percentage points, respectively. Ablations validate the complementary roles of session compilation and cross-session consolidation, while dynamics analyses reveal that the gate acquires task-specific memory integration strategies. These results establish RPMem as a lifecycle-independent parametric memory framework that maintains evolving cross-session memory that remains reusable across backbone replacements. Our implementation is available at https://github.com/Quark-Medical/rpmem/tree/main.

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