Parameter-Efficient Fine-Tuning (PEFT) methods have become crucial for rapidly adapting large language models (LLMs) to downstream tasks. Prefix-Tuning, an early and effective PEFT technique, demonstrated the ability to achieve performance comparable to full fine-tuning with significantly reduced computational and memory overhead. However, despite its earlier success, its effectiveness in training modern state-of-the-art LLMs has been very limited. In this work, we demonstrate empirically that Prefix-Tuning underperforms on LLMs because of an inherent tradeoff between the contribution of input prompt and parameterized prefix within the attention head. This motivates us to introduce PrefixMemory-Tuning, an architecture that generalizes the principles of Prefix-Tuning while addressing its shortcomings by shifting the prefix module out of the attention head itself and improving its expressiveness. Our experiments show that, across diverse benchmarks, PrefixMemory-Tuning consistently outperforms existing Prefix-Tuning methods. Notably, it achieves competitive performance with modern PEFTs on several general benchmarks, highlighting a potential extension of Prefix-Tuning approaches to become state-of-the-art. Our findings suggest that by overcoming its inherent limitations, Prefix-Tuning can remain a competitive and relevant research direction in the landscape of parameter-efficient LLM adaptation.