Long-duration gamma-ray flare (LDGRF) events observed by the Fermi/ Large Area Telescope have presented a puzzle for modelers. One of the ideas to account for their long duration is to assume that particles accelerated at shocks driven by fast coronal mass ejections (CMEs) would be the able to be trapped in the space between the shock and the Sun and would be able to precipitate from this volume over an extended amount of time. We present a simple leaky-box type model for the precipitating > 500 MeV proton flux in a system, where a coronal shock feeds accelerated protons into the volume between the shock and the solar surface and a relatively small amount of scattering keeps the distribution isotropic and homogeneous inside the volume. We demonstrate that by choosing fully realistic shock parameters the total number of precipitating protons can be brought to an agreement with observations. We also demonstrate that durations of several hours for these events are fully within reach of the modeling without using unreasonable choices for parameters. Thus, CME-driven shocks in the coronal and inner solar wind plasma are a plausible candidate to account for the LDGRF events.