Single-event upsets in the configuration memory of the 28-nm Xilinx Kintex-7 FPGA, used in the PANDA electromagnetic calorimeter, have been studied. Results from neutron and proton irradiations at energies up to 184 MeV are presented and compared with previous experimental results. In order to gain information about the energy-dependence of the single-event upset cross section, a GEANT4-based Monte Carlo simulation of upset mechanisms in nanometric silicon volumes has been developed. The results from this model are shown to agree with the experimental data for both neutrons and protons. Knowledge about the energy dependence of the cross section and of the particle flux at the location of the front-end modules in PANDA enables better estimates of the mean time between failures in the electromagnetic calorimeter. At PANDA, a total neutron flux of $1\cdot10^2$ cm$^{-2}$ s$^{-1}$ at the location of the front-end modules is expected at the lowest antiproton beam momentum and a luminosity of $1\cdot10^{31}$ cm$^{-2}$ s$^{-1}$, leading to a predicted Mean Time Between Failures of $47\pm10$ hours per FPGA in the electromagnetic calorimeter.