Although timing variations in close binary systems have been studied for a long time, their underlying causes are still unclear. A possible explanation is the so-called Applegate mechanism, where a strong, variable magnetic field can periodically change the gravitational quadrupole moment of a stellar component, thus causing observable period changes. One of the systems exhibiting such strong orbital variations is the RS CVn binary HR 1099, whose activity cycle has been studied by various authors via photospheric and chromospheric activity indicators, resulting in contradicting periods. We aim at independently determining the magnetic activity cycle of HR 1099 using archival X-ray data to allow for a comparison to orbital period variations. Archival X-ray data from 80 different observations of HR 1099 acquired with 12 different X-ray facilities and covering almost four decades were used to determine X-ray fluxes in the energy range of 2-10 keV via spectral fitting and flux conversion. Via the Lomb-Scargle periodogram we analyze the resulting long-term X-ray light curve to search for periodicities. We do not detect any statistically significant periodicities within the X-ray data. An analysis of optical data of HR 1099 shows that the derivation of such periods is strongly dependent on the time coverage of available data, since the observed optical variations strongly deviate from a pure sine wave. We argue that this offers an explanation as to why other authors derive such a wide range of activity cycle periods based on optical data. We conclude that our analysis constitutes the longest stellar X-ray activity light curve acquired to date, yet the still rather sparse sampling of the X-ray data, along with stochastic flaring activity, does not allow for the independent determination of an X-ray activity cycle.