We investigate the robustness of Whisper-based automatic speech recognition (ASR) models for two major Indonesian regional languages: Javanese and Sundanese. While recent work has demonstrated strong ASR performance under clean conditions, their effectiveness in noisy environments remains unclear. To address this, we experiment with multiple training strategies, including synthetic noise augmentation and SpecAugment, and evaluate performance across a range of signal-to-noise ratios (SNRs). Our results show that noise-aware training substantially improves robustness, particularly for larger Whisper models. A detailed error analysis further reveals language-specific challenges, highlighting avenues for future improvements.