Context : Recently , using the light-travel time effect , planets and sub-stellar companions have been proposed to orbit around binary star systems ( aka circumbinary companions ) as a result of variations in timing of observed eclipses .
For the majority of these systems the proposed orbital architecture features crossing orbital configurations as a result of high eccentricities for one , or both , of the companions .
For such systems , strong mutual gravitational interactions are expected , resulting in catastrophic orbital instabilities , or collisions between the proposed components , on very short timescales .

Aims : In this paper , we re-examine the primary and secondary eclipse timings of the short-period and semi-detached binary RZ Draconis ( RZ Dra ) , as originally presented in Yang et al .
( 2010 ) .
In their work , the proposed companions have masses of around \simeq 0.07 and \simeq 0.18 ~ { } M _ { \odot } with the inner companion on an orbit with moderate eccentricity ( 0.46 ) having its apocenter distance crossing the orbit of the outer companion .
We show that the companions proposed by Yang et al .
( 2010 ) follow highly unstable orbits .
In an attempt to find a stable system we have searched the underlying \chi ^ { 2 } parameter space for a best-fit model and carried out an orbital stability study in order to test possible best-fit models .
If the binary period changes are truly due to additional massive companions in a hierarchical configuration , they must follow stable orbits .

Methods : For numerical orbital stability calculations we use well-established orbit integration routines .
Computations were carried out using large-scale multi-CPU computing environment .
Data analysis of times of primary and secondary eclipse is based on the Levenberg-Marquardt least-squares minimisation algorithm using the two-body Keplerian light-travel time effect model .

Results : Despite the wide variety of potential models tested for the RZ Dra system in this work , we found very few models that were stable for even one million years , with the vast majority of systems tested falling apart on timescales of just hundreds of years .
It seems likely therefore , that the observed timing variations are not solely the result of massive , unseen companions .

Conclusions :