We investigated the temperature and pressure dependence of carrier recombination processes occurring in GaAsSb edge-emitting lasers operating near 1.3 mu m. Below similar to 100 K, the threshold current, I-th, is dominated by the radiative current, I-rad, and is proportional to temperature, T. However, above 100 K, non-radiative recombination increases abruptly such that by 125 K it accounts for 40% of I-th. From high pressure measurements at this temperature, we find that the non-radiative current decreases with increasing pressure, consistent with the presence of Auger recombination. At room temperature, non-radiative recombination accounts for similar to 90% I-th and gives rise to a super-linear temperature dependence of I-th, in spite of the fact that I-rad proportional to T. At room temperature the non-radiative current increases with increasing pressure, indicating that under ambient operating conditions, the devices are also limited by carrier leakage into the Gamma-minimum of the GaAs barriers and possibly also into the X-minima of the GaAsP confining layers.