This article reports on the long-term frequency stability characterization of a new type of cryogenic sapphire oscillator using an autonomous pulse-tube cryocooler as its cold source. This new design enables a relative frequency stability of better than 4.5 x 10(-15) over one day of integration. To the best of our knowledge, this represents the best long-term frequency stability ever obtained with a signal source based on a macroscopic resonator.