XSSJ1227.0-4859 is a peculiar, hard X-ray source recently positionally associated to the Fermi-LAT source 1FGLJ1227.9-4852/2FGLJ1227.7-4853. Multi-wavelength observations have added information on this source, indicating a low-luminosity low-mass X-ray binary (LMXB), but its nature is still unclear. To progress in our understanding, we present new X-ray data from a monitoring campaign performed in 2011 with the XMM-Newton, RXTE, and Swift satellites and combine them with new gamma-ray data from the Fermi and AGILE satellites. We complement the study with simultaneous near-UV photometry from XMM-Newton and with previous UV/optical and near-IR data. The X-ray history of XSSJ1227.0-4859 over 7yr shows a persistent and rather stable low-luminosity (~6x10^33 d_{1,kpc}^2 erg/s) source, with flares and dips being peculiar and permanent characteristics. The associated Fermi-LAT source 2FGLJ1227.7-4853 is also stable over an overlapping period of 4.7,yr. Searches for X-ray fast pulsations down to msec give upper limits to pulse fractional amplitudes of 15-25% that do not rule out a fast spinning pulsar. The combined UV/optical/near-IR spectrum reveals a hot component at ~13,kK and a cool one at ~4.6,kK. The latter would suggest a late-type K2-K5 companion star, a distance range of1.4--3.6kpc and an orbital period of 7--9 h. A near-UV variability (>6,h) also suggests a longer orbital period than previously estimated. The analysis shows that the X-ray and UV/optical/near-IR emissions are more compatible with an accretion-powered compact object than with a rotational powered pulsar. The X-ray to UV bolometric luminosity ratio could be consistent with a binary hosting a neutron star, but the uncertainties in the radio data may also allow an LMXB black hole with a compact jet. In this case it would be the first associated with a high-energy gamma-ray source.