"Sestina" addresses the passing of time by the change of season. The nifty thing is, in order to show that time moves on, Bishop actually shows us how it's cyclical. So we get the sense (especially from the sad grandmother) that time is moving on, but progress isn't necessarily being made. It's sort of a "no way out" feeling, which is only enhanced by the form of the poem.
The grandmother is freaked out by time passing because she thinks she's going to die soon and abandon the child.
The child is oblivious to the passage of time and goes on drawing happily with her crayons. She's not bummed at all—it's all the grandmother.