Detecting planetary companions around evolved stars, particularly asymptotic giant branch (AGB) stars, is challenging due to intrinsic stellar variability such as surface convection, pulsations, and mass loss, which can produce radial velocity (RV) signals that mimic Keplerian motion. We investigate the origin of the long-period, low-amplitude RV variations observed in the AGB star HD 216595 using high-resolution spectroscopic data spanning approximately 16 years obtained with the Bohyunsan Optical Astronomy Observatory Echelle Spectrograph (BOES) and the Las Cumbres Observatory Network of Robotic Echelle Spectrographs (NRES) instruments. The RV measurements reveal a statistically significant periodic signal with a period of 567 days that can be described by a Keplerian model consistent with a substellar companion. However, no strong correlations are found between the RV variations and stellar activity indicators, including line bisectors, chromospheric activity, and photometric variability, although weak signals on similar timescales are present in some diagnostics. Given the stellar properties of HD 216595 and its similarities to previously reported cases, the observed RV variations are likely related to intrinsic stellar processes, although a companion-induced origin cannot be definitively ruled out. Further progress will require improved diagnostics and more sophisticated modeling to disentangle stellar variability from genuine orbital signals.