  We use photometry and proper motions from Gaia DR2 to determine the blue
straggler star (BSS) populations of 16 old (1-10 Gyr), nearby ($d< 3500$ pc)
open clusters. We find that the fractional number of BSS compared to RGB stars
increases with age, starting near zero at 1 Gyr and flattening to $\sim 0.35$
by 4 Gyr. Fitting stellar evolutionary tracks to these BSS, we find that their
mass distribution peaks at a few tenths of a solar mass above the main-sequence
turnoff. BSS more than 0.5 $M_\odot$ above the turnoff make up only $\sim25$\%
of the sample, and BSS more than 1.0 $M_\odot$ above the turnoff are rare. We
compare this to population synthesis models of BSS formed via mass transfer
using the Compact Object Synthesis and Monte Carlo Investigation Code (COSMIC).
We find that standard population synthesis assumptions dramatically
under-produce the number of BSS in old open clusters. We also find that these
models overproduce high mass BSS relative to lower mass BSS. Expected numbers
of BSS formed through dynamics do not fully account for this discrepancy. We
conclude that in order to explain the observed BSS populations from Roche lobe
overflow, mass-transfer from giant donors must be more stable than assumed in
canonical mass-transfer prescriptions, and including non-conservative mass
transfer is important in producing realistic BSS masses. Even with these
modifications, it is difficult to achieve the large number of BSS observed in
the oldest open clusters. We discuss some additional physics that may explain
the large number of observed blue stragglers among old stellar populations.
