  Young stars show evidence of accretion discs which evolve quickly and
disperse with an e-folding time of $\sim$ 3Myr. This is in striking contrast
with recent observations that suggest evidence for numerous $>30$ Myr old stars
with an accretion disc in large star-forming complexes. We consider whether
these observations of apparently old accretors could be explained by invoking
Bondi-Hoyle accretion to rebuild a new disc around these stars during passage
through a clumpy molecular cloud. We combine a simple Monte Carlo model to
explore the capture of mass by such systems with a viscous evolution model to
infer the levels of accretion that would be observed. We find that a
significant fraction of stars may capture enough material via the Bondi-Hoyle
mechanism to rebuild a disc of mass $\gtrsim$ 1 minimum-mass solar nebula, and
$\lesssim 10\%$ accrete at observable levels at any given time. A significant
fraction of the observed old accretors may be explained with our proposed
mechanism. Such accretion may provide a chance for a second epoch of planet
formation, and have unpredictable consequences for planetary evolution.
