In this work we determine the Ne/O abundance ratio from Solar and Heliospheric Observatory (SOHO)/Solar Ultraviolet Measurement of Emitted Radiation (SUMER) off-disk observations of quiescent streamers over the 1996-2008 period. We find that the Ne/O ratio is approximately constant over solar cycle 23 from 1996 to 2005, at a value of 0.099 ± 0.017 this value is lower than the transition region determinations from the quiet Sun used to infer the neon photospheric abundance from the oxygen photospheric abundance. Also, the Ne/O ratio we determined from SUMER is in excellent agreement with in situ determinations from ACE/SWICS. In 2005-2008, the Ne/O abundance ratio increased with time and reached 0.25 ± 0.05, following the same trend found in the slowest wind analyzed by ACE/SWICS. Further, we measure the absolute abundance in the corona for both oxygen and neon from the data set of 1996 November 22, obtaining A o = 8.99 ± 0.04 and A Ne = 7.92 ± 0.03, and we find that both elements are affected by the first ionization potential (FIP) effect, with oxygen being enhanced by a factor of 1.4-2.1 over its photospheric abundance, and neon being changed by a factor of 0.75-1.20. We conclude that the Ne/O ratio is not constant in the solar atmosphere, both in time and at different heights, and that it cannot be reliably used to infer the neon abundance in the photosphere. Also, we argue that the FIP effect was less effective during the minimum of solar cycle 24, and that the Ne/O = 0.25 ± 0.05 value measured at that time is closer to the true photospheric value, leading to a neon photospheric abundance larger than assumed by ≈40%. We discuss the implications of these results for the solar abundance problem, for the FIP effect, and for the identification of the source regions of the solar wind.