Audio is a fundamental modality for analyzing speech, music, and environmental sounds. Although pretrained audio models have significantly advanced audio understanding, they remain fragile in real-world settings where data distributions shift over time. In this work, we present the first systematic benchmark for audio continual learning (CL) with pretrained models (PTMs), together with a comprehensive analysis of its unique challenges. Unlike in vision, where parameter-efficient fine-tuning (PEFT) has proven effective for CL, directly transferring such strategies to audio leads to poor performance. This stems from a fundamental property of audio backbones: they focus on low-level spectral details rather than structured semantics, causing severe upstream-downstream misalignment. Through extensive empirical study, we identify analytic classifiers with first-session adaptation (FSA) as a promising direction, but also reveal two major limitations: representation saturation in coarse-grained scenarios and representation drift in fine-grained scenarios. To address these challenges, we propose PACE, a novel method that enhances FSA via a regularized analytic classifier and enables multi-session adaptation through adaptive subspace-orthogonal PEFT for improved semantic alignment. In addition, we introduce spectrogram-based boundary-aware perturbations to mitigate representation overlap and improve stability. Experiments on six diverse audio CL benchmarks demonstrate that PACE substantially outperforms state-of-the-art baselines, marking an important step toward robust and scalable audio continual learning with PTMs.