The deployment of large language models (LLMs) on resource-constrained devices remains challenging, spurring interest in split inference, where models are partitioned between client and server to reduce computational burden and enhance privacy by transmitting only intermediate activations. However, the privacy-preserving capabilities of split inference, particularly in the context of LLMs, have not been exhaustively investigated. To fill this gap, we introduce ActInv, which solves an intermediate activation matching problem to reconstruct the client's input. Extensive evaluations demonstrate that ActInv achieves high-fidelity reconstructions, even in the presence of common perturbation-based defenses such as Gaussian noise injection and activation sparsification. To systematically understand this vulnerability, we develop Perturbation Amplification Factor (PAF), a metric for quantifying a layer's inherent resistance to reconstruction. Our analysis reveals that privacy vulnerability is not uniform across layers, with some layers being highly susceptible to leakage while others offer natural resistance. Furthermore, we demonstrate that defense effectiveness can be significantly improved by calibrating perturbation directions to maximize reconstruction error during backpropagation. Building on these insights, we design PriPert and conduct comprehensive evaluations, covering privacy, utility, and computational overhead, to demonstrate its effectiveness.