Automatic Program Repair (APR) has garnered significant attention as a practical research domain focused on automatically fixing bugs in programs. While existing APR techniques primarily target imperative programming languages like C and Java, there is a growing need for effective solutions applicable to declarative software specification languages. This paper systematically investigates the capacity of Large Language Models (LLMs) to repair declarative specifications in Alloy, a declarative formal language used for software specification. We designed 12 different repair settings, encompassing single-agent and dual-agent paradigms, utilizing various LLMs. These configurations also incorporate different levels of feedback, including an auto-prompting mechanism for generating prompts autonomously using LLMs. Our study reveals that dual-agent with auto-prompting setup outperforms the other settings, albeit with a marginal increase in the number of iterations and token usage. This dual-agent setup demonstrated superior effectiveness compared to state-of-the-art Alloy APR techniques when evaluated on a comprehensive set of benchmarks. This work is the first to empirically evaluate LLM capabilities to repair declarative specifications, while taking into account recent trending LLM concepts such as LLM-based agents, feedback, auto-prompting, and tools, thus paving the way for future agent-based techniques in software engineering.