In this paper, we study the time consistency of cooperative agreements in dynamic games with nontransferable utility. An agreement designed at the outset of a game is time consistent (or sustainable) if it remains in place for the entire duration of the game, that is, if no player would benefit from switching to his Nash equilibrium strategy. The literature has highlighted that, since side payments are not allowed, the design of such an agreement is very challenging. To address this issue, we introduce different notions for the temporal stability of an agreement and characterize the agreement's intrinsic longevity. We illustrate our general results with a linear-quadratic difference game and show that an agreement's longevity can be easily assessed using the problem data. We also study the effect of information structure on the longevity of the agreement. We illustrate our results with a numerical example.