Vision-Language-Action (VLA) models have achieved remarkable success in language-conditioned robotic manipulation. However, deploying these models in open-ended environments requires continuously acquiring novel skills, a process that inevitably triggers severe catastrophic forgetting of previously learned behaviors. While experience replay (ER) serves as a standard mitigating strategy, naive uniform sampling fundamentally misaligns with the temporal characteristics of manipulation trajectories. It systematically under-samples brief but causally critical sub-skills, leading to phase starvation, and completely overlooks the varying degrees of forgetting across historical tasks. To overcome these limitations, we introduce PHASER, an architecture-agnostic continual learning framework. PHASER employs a phase-centric capacity allocation to guarantee equal memory support for all sub-skills, coupled with a multi-modal interference routing strategy that dynamically prioritizes historical phases at high risk of forgetting. Furthermore, to enable fully autonomous lifelong adaptation, we integrate Auto-PC, a lightweight pipeline combining unsupervised action-signal change-point detection with VLM-based semantic verification to extract temporal boundaries without intensive manual supervision. Evaluated across three VLA backbones on LIBERO continual learning suites, PHASER yields substantial empirical improvements, increasing Average Success Rate (ASR) by up to 31% over matched-budget ER and achieving an 87.8% final ASR on the LIBERO-Goal CL setting.