The cyclic behavior of (O-C) residuals of eclipse timings in the sdB+M eclipsing binary NSVS 14256825 was previously attributed to one or two Jovian-type circumbinary planets. We report 83 new eclipse timings that not only fill in the gaps in those already published but also extend the time span of the (O-C) diagram by three years. Based on the archival and our new data spanning over more than 17 years, we re-examined the up-to-date system (O-C). The data revealed a systematic, quasi-sinusoidal variation deviating from an older linear ephemeris by about 100 s. It also exhibits a maximum in the (O-C) near JD 2456400 that was previously unknown. We consider two most credible explanations of the (O-C) variability: the light propagation time due to the presence of an invisible companion in a distant circumbinary orbit, and magnetic cycles reshaping one of the binary components, known as the Applegate or Lanza-Rodono effect. We found that the latter mechanism is unlikely due to the insufficient energy budget of the M-dwarf secondary. In the framework of the third-body hypothesis, we obtained meaningful constraints on the Keplerian parameters of a putative companion and its mass. Our best-fitting model indicates that the observed quasi-periodic (O-C) variability can be explained by the presence of a brown dwarf with the minimal mass of 15 Jupiter masses rather than a planet, orbiting the binary in a moderately elliptical orbit (e~0.175) with a period of ~10 years. Our analysis rules out the two-planet model proposed earlier.