We introduce a novel self-improving framework that enhances Embodied Visual Tracking (EVT) with Vision-Language Models (VLMs) to address the limitations of current active visual tracking systems in recovering from tracking failure. Our approach combines the off-the-shelf active tracking methods with VLMs' reasoning capabilities, deploying a fast visual policy for normal tracking and activating VLM reasoning only upon failure detection. The framework features a memory-augmented self-reflection mechanism that enables the VLM to progressively improve by learning from past experiences, effectively addressing VLMs' limitations in 3D spatial reasoning. Experimental results demonstrate significant performance improvements, with our framework boosting success rates by $72\%$ with state-of-the-art RL-based approaches and $220\%$ with PID-based methods in challenging environments. This work represents the first integration of VLM-based reasoning to assist EVT agents in proactive failure recovery, offering substantial advances for real-world robotic applications that require continuous target monitoring in dynamic, unstructured environments. Project website: https://sites.google.com/view/evt-recovery-assistant.