Optical chaos is easily observed in a laser diode with either conventional (COF) or phase-conjugate optical feedback (PCF). We focus here on the so-called chaotic low-frequency fluctuations (LFF) where the laser exhibits slow power dropouts together with fast picosecond dynamics. We report here on a systematic study of LFF in a laser diode when subjected to PCF for which the bifurcations leading to those LFF remain to be elucidated. Qualitatively different dynamics are observed when increasing the phase-conjugate mirror (PCM) reflectivity or the injection current level. A combination of spectral and temporal measurements unveils the transition to LFF dynamics. The statistical properties of the time between power dropouts -mean dropout time and standard deviation- are studied as a function of the laser and feedback parameters and show that the laser may undergo what we call here a deterministic coherence resonance for a particular value of the PCF ratio. Interestingly, the phase conjugation build-up time here in SPS crystal is around 3 ms, hence is three orders of magnitude faster than what has been reported in previous dynamical studies of chaos in lasers with PCF using BaTiO3 photorefractive crystals. How the phase conjugation time-scale impacts on the laser dynamics remains an interesting question to which we contribute here.