Remember that Abaqus is designed for non-linear dynamic analysis. Naturally when the loads has a history and are sustained, then deformations are in progress. As a results, all input and stored energies are time dependent.
If you are doing linear static analysis. Internal forces and the external forces are in equilibrium and there no further change in the state of the system. In such, all energies have a final value.
When a system under a dynamic load comes to rest ( i.e. there is no loading any more), the system may partially or totally recover (no permanent deformation or residual stresses), then the final values of energies are also constant.