Maintaining preload in bolted joints is critical for the safe and efficient operation of nearly all built-up structures. Dynamic loss of preload during operation occurs when sufficient shear force is applied to the joint such that slip is induced in at least the threads if not the entire bolt. Such shear forces are often realized when the joint is subjected to sustained vibrations, resulting in loosening over relatively long periods of time, or extreme shock loading where loosening occurs over fractions of a second. Modeling of joint loosening often focuses on complex analytical approaches or high-fidelity simulations using finite element models. While such approaches may succeed for a single bolt, they are unfeasible for use in simulations of entire built-up structures, which may possess dozens to thousands of joints. Thus, there is a need for reduced-order models (ROMs) that capture the dominant governing physics, but at drastically lower computational costs. This research introduces a phenomenological ROM for loosening in bolted joints subjected to axial shock excitation. The model introduces a mathematical relationship between the stiffness of the joint and torque of the fastener and treats the torque as a dynamic internal variable governed by a first-order, ordinary differential equation. The proposed ROM is presented then applied to an experimental study of a split-Hopkinson pressure bar with a threaded joint subjected to extreme shock loading. The results demonstrate that the proposed ROM is able to reproduce the dominant effects of loosening in bolted joints subjected to axial shock excitation.