The widespread use of publicly available pre-trained encoders from self-supervised learning (SSL) has exposed a critical vulnerability: their susceptibility to downstream-agnostic adversarial examples (DAEs), which are crafted without knowledge of the downstream tasks but capable of misleading downstream models. While several defense methods have been explored recently, they rely primarily on task-specific adversarial fine-tuning, which inevitably limits generalizability and causes catastrophic forgetting and deteriorates benign performance. Different with previous works, we propose a more rigorous defense goal that requires only a single tuning for diverse downstream tasks to defend against DAEs and preserve benign performance. To achieve this defense goal, we introduce Zero-Sacrifice Persistent-Robustness Adversarial Defense (ZePAD), which is inspired by the inherent sensitivity of neural networks to data characteristics. Specifically, ZePAD is a dual-branch structure, which consists of a Multi-Pattern Adversarial Enhancement Branch (MPAE-Branch) that uses two adversarially fine-tuned encoders to strengthen adversarial resistance. The Benign Memory Preservation Branch (BMP-Branch) is trained on local data to ensure adversarial robustness does not compromise benign performance. Surprisingly, we find that ZePAD can directly detect DAEs by evaluating branch confidence, without introducing any adversarial exsample identification task during training. Notably, by enriching feature diversity, our method enables a single adversarial fine-tuning to defend against DAEs across downstream tasks, thereby achieving persistent robustness. Extensive experiments on 11 SSL methods and 6 datasets validate its effectiveness. In certain cases, it achieves a 29.20% improvement in benign performance and a 73.86% gain in adversarial robustness, highlighting its zero-sacrifice property.