  All of the known circumbinary planets are large (> 3 Earth radii). Whilst
observational biases may account for this dearth of small planets, in this
paper we propose a theoretical explanation. Most of the known planets are near
the stability limit, interspersed between potentially unstable 5 : 1, 6 : 1 and
7 : 1 mean motion resonances with the binary. It is believed that these planets
did not form in situ, but rather migrated from farther out in the disc, and
hence passed through these resonances. Planets are expected to migrate at a
speed proportional to their mass, and a slower rate makes resonant capture and
subsequent ejection more likely. Therefore, whilst large planets may be able to
successfully "run the gauntlet", small planets may be imperiled. This
hypothesis is tested using N-body integrations of migration in a truncated and
turbulent disc. We discover that surprisingly none of the known planets exist
interior to a fully unstable resonance. We demonstrate that resonant ejection
of migrating planets may occur in nature, and that it does indeed
disproportionately affect small planets, but it requires a highly turbulent
disc and its efficiency is likely too low to fully explain a dearth of < 3
Earth radii planets.
