Heart rate (HR) fluctuations provide a well-known example of fractal stochastic dynamics of physiological functions with a 1/f power spectrum. So far, this type of HR behavior has been documented for the frequency range 0.1-10 mHz. In this paper, we report the results of a case study based on a long-term HR monitoring performed during a period of 38 months. The analyzed database consisted of over 1200 samples of R-R interval fluctuations of single person with the average sample duration of 10 minutes and average inter-sample time interval 1 day. For each of the 10-minute samples, a set of statistical and nonlinear parameters has been evaluated based on the FFT spectral analysis and the detrended fluctuation analysis technique. It has been found that time series of many of the studied parameters (mean value and standard deviation of R-R interval, spectral power of R-R fluctuations in standard frequency bands of clinical HR variability analysis, etc.) demonstrate extra-low frequency organization involving frequency range 0.00005-0.005 mHz (time scales 20 to 200 days) . The revealed correlations manifest themselves in a 1/f-like spectral behavior similar to the behavior detected earlier at considerably shorter time scales of HR fluctuations. Participation of the central nervous system in the extra slow HR variations has been confirmed experimentally and shown to reflect long-term adaptation dynamics of human homeostasis in a complex fluctuating environment.