Additively manufactured composite tools are increasingly used in sheet forming, yet the influence of fiber orientation on tool durability remains poorly understood. In this context, the present study investigates the limited understanding of how different continuous-fiber deposition strategies affect the mechanical stability and durability of additively manufactured polymer punches for deep drawing. Polymer tools reinforced with continuous carbon fibers were fabricated using continuous fiber fabrication (CFF) with two reinforcement layouts—concentric and isotropic—and tested until fracture to assess the achievable drawing depth, punch deformation, and cup integrity. Failure onset was monitored and the dimensional stability of the produced cups was evaluated as indicators of tool performance. The results demonstrated that fiber reinforcement increased the maximum drawable depth from 15 mm (unreinforced onyx punch) to 18 mm for concentric and 19 mm for isotropic punches. Finite element simulations reproduced the deformation trends observed experimentally, confirming that concentric reinforcement leads to higher axial compression and radial expansion. The findings highlight the potential of CFF for producing lightweight, low-cost forming tools, underscoring that optimizing fiber orientation is critical for improving tool durability and process repeatability.