KIC 8677585 is a roAp star in the Kepler field which is unique in that there are four low-frequency variations of unknown origin in addition to more than 20 high-frequency roAp modes. We analysed all available spectroscopy and conclude that the star has a constant radial velocity and most likely not a binary. We estimate its effective temperature to be Teff = 7300 ± 200 K from high-dispersion spectra. We present an analysis of 829 d of Kepler short-cadence data which shows clear frequency and amplitude variations with a time-scale of months. The dominant low-frequency peak at 3.142 d-1 has the same frequency and amplitude variation as one of the roAp modes. We therefore conclude that the low frequencies are oscillations in the roAp star itself, but the driving mechanism is unknown. We find several frequency spacings among the roAp modes equal to the dominant low frequency, suggestive of non-linear interactions. There is also a clear spacing of 37.2 μHz which we interpret as the large separation and deduce that log g = 3.90 ± 0.03. Models with these parameters which take into account the effect of the magnetic field on the oscillations are able to reproduce the observed range of roAp frequencies, but not the observed large separation. It is found that the properties of the oscillations are sensitive to the assumed stellar parameters and that a more detailed analysis is required. The fact that low frequencies are closely coupled to the roAp frequencies calls into question our current understanding of pulsation in these stars.