  Transiting circumbinary planets are more easily detected around short-period
than long-period binaries, but none have yet been observed by {\it Kepler}
orbiting binaries with periods shorter than seven days. In triple systems,
secular Kozai-Lidov cycles and tidal friction (KLCTF) have been shown to reduce
the inner orbital period from $\sim 10^4$ to a few days. Indeed, the majority
of short-period binaries are observed to possess a third stellar companion.
Using secular evolution analysis and population synthesis, we show that KLCTF
makes it unlikely for circumbinary transiting planets to exist around
short-period binaries. We find the following outcomes. (1) Sufficiently massive
planets in tight and/or coplanar orbits around the inner binary can quench the
KL evolution because they induce precession in the inner binary. The KLCTF
process does not take place, preventing the formation of a short-period binary.
(2) Secular evolution is not quenched and it drives the planetary orbit into a
high eccentricity, giving rise to an unstable configuration, in which the
planet is most likely ejected from the system. (3) Secular evolution is not
quenched but the planet survives the KLCTF evolution. Its orbit is likely to be
much wider than the currently observed inner binary orbit, and is likely to be
eccentric and inclined with respect to the inner binary. These outcomes lead to
two main conclusions: (1) it is unlikely to find a massive planet on a tight
and coplanar orbit around a short-period binary, and (2) the properties of
circumbinary planets in short-period binaries are constrained by secular
evolution.
