The annihilation of light dark matter was recently advocated as a possible explanation of the large positron injection rate at the Galactic center deduced from observations by the SPI spectrometer aboard INTEGRAL. The modelling of internal Bremsstrahlung and in-flight annihilation radiations associated to this process drastically reduced the mass range of this light dark matter particle. We estimate critically the various energy losses and radiations involved in the propagation of the positron before its annihilation --in- flight or at rest. Using a simple model with mono-energetic positrons injected and confined to the Galactic bulge, we compute energy losses and gamma-ray radiations caused by ionization, Bremsstrahlung interactions as well as in-flight and at rest annihilation and compare these predictions to the available observations, for various injection energies. Confronting the predictions with observations by the CGRO/EGRET, CGRO/COMPTEL, INTEGRAL/SPI and INTEGRAL/IBIS/ISGRI instruments, we deduce a mass upper bound of 3 to 7.5 MeV/c^2 for the hypothetical light dark matter particle. The most restrictive limit is in agreement with the value previously found by Beacom and Yuksel and was obtained under similar assumptions, while the 7.5 MeV/c^2 value corresponds to more conservative choices and to a partially ionized propagation medium. We stress how the limit depends on the degree of ionization of the propagation medium and how its precision could be improved by a better appraisal of data uncertainties.
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