Homomorphic Encryption (HE) enables computation on encrypted data without decryption, making it a cornerstone of privacy-preserving computation in untrusted environments. As HE sees growing adoption in sensitive applications such as secure machine learning and confidential data analysis ensuring its robustness against errors becomes critical. Faults (e.g., transmission errors, hardware malfunctions, or synchronization failures) can corrupt encrypted data and compromise the integrity of HE operations. However, the impact of soft errors (such as bit flips) on modern HE schemes remains unexplored. Specifically, the CKKS scheme-one of the most widely used HE schemes for approximate arithmetic-lacks a systematic study of how such errors propagate across its pipeline, particularly under optimizations like the Residue Number System (RNS) and Number Theoretic Transform (NTT). This work bridges that gap by presenting a theoretical and empirical analysis of CKKS's fault tolerance under single bit-flip errors. We focus on client-side operations (encoding, encryption, decryption, and decoding) and demonstrate that while the vanilla CKKS scheme exhibits some resilience, performance optimizations (RNS/NTT) introduce significant fragility, amplifying error sensitivity. By characterizing these failure modes, we lay the groundwork for error-resilient HE designs, ensuring both performance and integrity in privacy-critical applications.