Recent advances in Large Reasoning Models (LRMs) are reshaping reasoning-intensive reranking, where step-by-step reasoning enables multi-faceted relevance judgments. To scale LRMs, existing approaches distill chain-of-thought traces from a teacher LRM into a student reranker via Supervised Fine-Tuning (SFT) followed by Reinforcement Learning (RL). However, this pipeline is misaligned with the distillation objective: teacher traces are too dense for direct imitation, while RL exploration is too sparse on hard cases. To this end, we propose SARD (Self-Adaptive Reinforced Distillation), a tri-mode RL framework that recasts teacher reasoning from a fixed supervision target into an adaptive resource the student draws on only when its own reasoning falls short. Triggered by rollout outcomes, SARD organizes training into three modes: Free Exploration, where the student reasons independently; Guided Exploration, which supplies reusable in-context guidance abstracted from teacher traces when free rollouts fail; and Teacher-Guided Repair, where the teacher diagnoses failures and revises, re-selects, or appends guidance, falling back to teacher trajectories only as a last resort. Experiments on reasoning-intensive reranking benchmarks show SARD outperforms strong reranking and SFT-then-RL baselines, with clear gains on difficult instances and under-represented reasoning patterns.