The energy spectra of galactic cosmic rays carry fundamental information regarding their origin and propagation. These spectra, when measured near Earth, are significantly affected by the solar magnetic field. A comprehensive description of the cosmic radiation must therefore include the transport and modulation of cosmic rays inside the heliosphere. During the end of the last decade, the Sun underwent a peculiarly long quiet phase well suited to study modulation processes. In this paper we present proton spectra measured from 2006 July to 2009 December by PAMEFA. The large collected statistics of protons allowed the time variation to be followed on a nearly monthly basis down to 400 MV. Data are compared with a state-of-the-art three-dimensional model of solar modulation.