We present multi-epoch photometric and spectroscopic near-infrared observations of the Be star X Persei in the JHK bands covering the wavelength range 1.08 to 2.35 micron. Combining results from our earlier studies with the present observations, it is shown that the equivalent widths and line fluxes of the prominent HI and HeI lines anti-correlate with the strength of the adjacent continuum. That is, during the span of the observations, the JHK broad band fluxes increase while the emission equivalent width values of the HI and HeI lines decrease (the lines under consideration being the Paschen and Brackett lines of hydrogen and the 1.7002 micron and 2.058 micron lines of helium). Such an anti-correlation effect is not commonly observed in Be stars in the optical; in the infrared this may possibly be the first reported case of such behavior. We examine different mechanisms that could possibly cause it and suggest that it could originate due to a radiatively warped, precessing circumstellar disk. It is also shown that during the course of our studies X Per evolved to an unprecedented state of high near-IR brightness with J, H, K magnitudes of 5.20, 5.05 and 4.84 respectively.