In the last decades the important increase of the number of positioning satellite constellations (GNSS, Global Navigation Satellite System), such as GPS, GLONASS, BeiDou and Galileo, has motivated a growing interest in the dynamics of the Medium Earth Orbits (MEOs). Numerical experiments show that resonances can affect the stability of MEOs; these resonances are due to a third body (the Moon or the Sun) perturbation that becomes significant for medium and high altitudes. In this work we investigate the effect of the solar perturbation and of the resulting resonances, on the stability of high MEOs (semi-major axis greater than 20000 km). We build an Hamiltonian model suitable for a large class of resonances and use it to study analytically and numerically the stability around one particular resonance, affecting orbits close to the operational Galileo orbits. We focus in particular on the evolution of the eccentricity which is of fundamental importance to ensure that orbit crossings do not occur. An important conclusion is that for some initial conditions, the eccentricity can experience very large excursions (up to 0.8 for the considered resonance) making orbit crossings possible.