  We present further observational data of the supersoft X-ray source RX
J0527.8-6954 exhibiting a continuous decline over the past 5 yrs. With no clear
trend of a concordant temperature decrease this might suggest an evolutionary
scenario where the white dwarf leaves the steady burning branch and the
combined effect of reduced luminosity and cooling at constant radius produces
the observed effect. We also use the on-axis ROSAT HRI pointings to derive an
improved X-ray position and supply a finding chart for the counterpart search.
