SDSS J1021+1744 is a detached, eclipsing white dwarf/M dwarf binary discovered in the Sloan Digital Sky Survey (SDSS). Outside the primary eclipse, the light curves of such systems are usually smooth and characterized by low-level variations caused by tidal distortion and heating of the M star component. Early data on SDSS J1021+1744 obtained in 2012 June were unusual in showing a dip in flux of uncertain origin shortly after the white dwarf's eclipse. Here we present high-time resolution, multiwavelength observations of 35 more eclipses over 1.3 yr, showing that the dip has a lifetime extending over many orbits. Moreover the `dip' is in fact a series of dips that vary in depth, number and position, although they are always placed in the phase interval 1.06-1.26 after the white dwarf's eclipse, near the L5 point in this system. Since SDSS J1021+1744 is a detached binary, it follows that the dips are caused by the transit of the white dwarf by material around the Lagrangian L5 point. A possible interpretation is that they are the signatures of prominences, a phenomenon already known from H α observations of rapidly rotating single stars as well as binaries. What makes SDSS J1021+1744 peculiar is that the material is dense enough to block continuum light. The dips appear to have finally faded out around 2015 May after the first detection by Parsons et al. in 2012, suggesting a lifetime of years.