The detection of pulsations from an X-ray binary is an unambiguous signature of the presence of a neutron star in the system. When the pulsations are missed in the radio band, their detection at other wavelengths, such as X-ray or gamma-rays, requires orbital demodulation, since the length of the observations is often comparable to, or longer than, the system orbital period. A detailed knowledge of the orbital parameters of binary systems plays a crucial role in the detection of the spin period of pulsars since any uncertainty in their determination translates into a loss in the coherence of a signal during the demodulation process. In this paper, we present an analytical study aimed at unveiling how the uncertainties in the orbital parameters might impact on periodicity searches. We find a correlation between the power of the signal in the demodulated arrival time series and the uncertainty in each of the orbital parameters. This correlation is also a function of the pulsar frequency. We test our analytical results with numerical simulations, finding good agreement between them. Finally, we apply our study to the cases of LS 5039 and LS I +61 303 and consider the current level of uncertainties in the orbital parameters of these systems and their impact on a possible detection of a hosted pulsar. We also discuss the possible appearance of a sideband ambiguity in real data. The latter can occur when, due to the use of uncertain orbital parameters, the power of a putative pulsar is distributed in frequencies lying near the pulsar period. Even if the appearance of a sideband is already a signature of a pulsar component, it may introduce an ambiguity in the determination of its period. We present here a method to solve the sideband issue.