The time dependent rheo-mechanical properties of a class of associating polymers (amine-functionalized polyolefins) are investigated using rheology, differential scanning calorimetry (DSC), infrared microscopy, and small-angle x-ray scattering (SAXS) measurement. The modulus of the sample increases with time and temperature as determined by shear rheology. With higher temperature and longer equilibration time, there is a gradual decrease in the power-law scaling of storage and loss moduli in the terminal flow region and the emergence of an additional low-frequency plateau in the storage modulus. The aging behavior at different temperatures is found to be correlated with the horizontal shift factors obtained from the time-temperature superposition. With increasing aging time, there is an increase in the glass transition temperatures (DSC), and a continuous red shift in the associated amine stretching peak (Fourier-transform infrared). SAXS also shows the emergence of a dominant microstructure after aging of the sample for a long time. Based on the characterization results, an underlying microscopic origin of the aging process is proposed.