Online continual learning requires models to learn from non‑stationary data streams while retaining prior knowledge. We identify an overlooked phenomenon—knowledge fragility—where correctly learned instances are rapidly forgotten after minor parameter updates. Our analysis attributes this fragility to a temporal–spatial dual mechanism: temporal instability, high-frequency parameter oscillations cause forgetting to outpace adaptation; and spatial vulnerability, fragile instances lie in sharp, high‑curvature regions of the loss landscape that are extremely sensitive to optimization noise. These insights motivate PDFK (Perturbing to Defend Fragile Knowledge), a unified framework that defends fragile knowledge along both dimensions. Temporally, we apply exponential moving averaging to smooth parameter evolution and stabilize long‑term memory. Spatially, we inject minimal structured perturbations with a consistency constraint to flatten sharp regions and enhance robustness. PDFK requires no task‑boundary annotations. Extensive experiments demonstrate that PDFK substantially improves knowledge retention and outperforms strong baselines under diverse and challenging continual learning settings.