Federated Learning (FL) is a collaborative machine learning paradigm for training models on local sensitive data with privacy protection. Pre-trained transformer-based models have emerged as useful foundation models (FMs) to be fine-tuned for a wide range of downstream tasks. However, large-scale pre-trained models make it challenging for traditional FL due to high communication overhead in the resource-constrained IoT. This has inspired the field of parameter-efficient fine-tuning (PEFT) research. Existing PEFT methods attempt to optimize model performance at the given dropout level. Such an approach places the burden on human users to find a dropout rate that provides a satisfactory level of performance through trial-and-error, which is time consuming and resource intensive. To address this limitation, we propose the Step-wise Parameter Dropout for Continual Federated Learning (SPD-CFL) approach. Instead of pre-defining a desired dropout rate, it allows users to specify the target level of performance and then attempts to find the most suitable dropout rate for the given FL model. Specifically, on the server side, SPD-CFL drops trainable parameters in a stepwise manner to improve communication efficiency by reducing the rank of low-rank adaptation (LoRA). The sensitivity-based gradient consistency (SGC) measure is designed to facilitate the adaptive adjustment of parameter dropout. In addition, SPD-CFL introduces continual learning (CL) on the client side to mitigate performance degradation due to the inconsistent optima with distinct parameter dropout rates under heterogeneous FL. Extensive experiments on the public benchmark dataset CIFAR-10 and a real-world medical Face dataset demonstrate significant superiority of SPD-CFL over state-of-the-art methods. Compared to the best-performing baseline, it achieves a 2.07% higher test AUC while reducing communication overhead by 29.53%.