Non-traditional machining methods like wire electric discharge machining (WEDM) appear to be an ideal choice for machining high strength super alloys like Inconel 706, because of their capability to generate intricate profiles with high accuracy. However, wire breakages are a common problem in the WEDM process and adversely affect the productivity, accuracy, and surface quality. Therefore, the aim of this work is to investigate and comprehend the phenomenon of wire breakage using Inconel 706 as work material and brass wire, diffused brass wire, and zinc-coated brass wire as electrode materials. Six process parameters—pulse-on time, pulse-off time, peak current, spark gap voltage, wire feed rate, and wire tension—have been varied experimentally to determine their effect on the frequency of wire failure. According to the findings, the zinc-coated brass wire breaks with the lowest frequency when compared to the other two. Additionally, an ideal range of input variables has been proposed for efficient WEDM of Inconel 706 without unexpected wire breakages. This range can also be utilized for further research work related to modeling and optimization in WEDM of Inconel 706.