The propagation characteristics of ion-acoustic negative solitons, in a multi-component plasma with negative ions, are investigated considering a kinetic model which takes into account electron reflection and positive ion trapping in the negative potential well of the soliton. The Poisson equation is solved consistently using the Sagdeev potential formalism (1966). It is verified that the kinetic effects associated with trapping of positive ions and reflection of electrons modify the results predicted by the simple Korteweg-de Vries fluid model in such a way that the Mach number is reduced as the ion temperature and the population of reflected electrons increase. Comparison with experimental observations shows that the measured values of the Mach number can be reproduced by this kinetic model under proper selection of the ion temperature and the shape of the reflected electron distribution function with a dependence on the negative ion concentration.