The Karlsruhe Tritium Neutrino experiment (KATRIN) is targeted to measure $m(\nu_e)$ with a sensitivity of 200 meV (90% C.L.). To determine the neutrino mass, the integrated $\beta$-spectrum of tritium is measured close to the endpoint and a fit to the data, comprising the neutrino mass as a free parameter, is performed. A number of systematic effects need to be taken into account in the analysis. One of the major effects is the energy loss from inelastic scattering of beta-electrons with the source gas. The corresponding energy loss function can be measured by means of an electron gun producing quasi-monoenergetic electrons at 18.6 keV with very small angular spread both in cw and pulsed mode. A new semi-empirical model has been developed based on the experimental data. This contribution presents the new model and its impact on the KATRIN neutrino mass sensitivity.