Elastic moduli are fundamental thermodynamic susceptibilities that connect directly to thermodynamics, electronic structure and mechanic properties. It is important to determine the origin of changes in elastic properties in 239Pu and its Ga alloys as a function of time. The most-likely sources of these changes include a) ingrowth of radioactive decay products like He and U, b) the introduction of radiation damage, c) δ-phase instabilities towards α-Pu or to Pu3Ga. The measurement of mechanical resonance frequencies can be made with extreme precision and used to compute the elastic moduli without corrections giving important insight in this problem. Using Resonant Ultrasound Spectroscopy, time-dependent measurements were made of the mechanical resonance frequencies of fine-grained polycrystalline δ-phase 239Pu, from room temperature up to 480K. At room temperature, both shear (G) and bulk (B) moduli increase in time with the rate of G at least a factor of 3 faster than that of B. As the temperature is increased, the rates of change increase exponentially with both G and B becoming stiffer with time. For T>420K an abrupt change in the time dependence is observed indicative of different G and B time dependence, however no changes in rate are observed when the temperature (400K) corresponding to the α-β lines is crossed. These measurements suggest that the changes in time observed in Ga-stabilized δ-239Pu are consistent with the thermally activated creation of defects, that can be (partially) annealed for T>420K. Our measurements also rule out the decomposition of δ-Pu(Ga) towards α-Pu or Pu3Ga as the main source of changes in δ-Pu in laboratory time frame.