Tool-augmented large language model (LLM) agents rely on orchestration layers that coordinate planning, retrieval, tool invocation, validation, memory, and recovery. In these systems, failures arise not only from model errors, but also from orchestration-level issues such as tool timeouts, malformed arguments, stale context, contradictory evidence, retry loops, and unverified intermediate outputs. This paper presents a self-healing agentic orchestrator that treats reliability as a bounded runtime control problem. The orchestrator maps observable failure signals to inferred failure classes, selects targeted recovery actions under explicit budgets, verifies recovered trajectories, and records observability traces. We evaluate the approach on a 100-task controlled fault-injection benchmark against static workflow, retry-only, ReAct-style, and full-replanning baselines. Self-healing achieves 98.8\% task success, compared with 94.5\% for retry-only and 93.8\% for full replanning. A matched recovery-budget sweep shows that self-healing outperforms retry-only and full replanning at every tested budget, with the largest gap under a single recovery attempt: 94.0\% versus 85.3\% and 88.2\%, respectively. Under a controlled semantic silent-failure setting, verifier-guided self-healing reduces silent failures to 0.0\%, while non-verifying baselines return wrong-but-plausible outputs more often. A compact model-in-the-loop validation shows that the same recovery mechanism can operate when a live tool-calling model performs tool selection, argument generation, and answer synthesis over local fault-injected tools. These results provide controlled evidence that failure-aware, budgeted, and verification-guided orchestration improves reliability and diagnosability in tool-augmented LLM systems.