FUSE observations were obtained in July 2003 during 1.2 cycles of the 0.76-day binary orbit of RX J0513.9-6951. Radial velocity measurements of the broad O VI emission profile show a semiamplitude of K~26 km/sec, which is much smaller than the value of 117 km/sec measured from 2001 FUSE data. Narrow O VI emissions show no measurable velocity variation. The mean velocity of the broad O VI emission is red-shifted by ~500 km/sec with respect to both the systemic and narrow emission-line velocities. Spectral difference plots show phase-related changes in the broad emission profile. Other phase-related changes such as line and continuum variations are also smaller than in the 2001 spectra. We describe a moving broad absorption feature near 1020A as possible O VI outflow associated with a precessing jet. We discuss the implications for the stellar masses if the 2003 broad O VI velocities outline the compact stars orbital motion.