If your grandmother is always talking about how quickly the years go by, she is focused on life's transience, or briefness.
Summer's quality of seeming to be over just as it's started can be described as transience — anything that feels impossibly brief has that same attribute. People most often use the noun transience when they're talking about good things, like beautiful days, a nice life, or a fun vacation, that seem to be over in an instant. The word comes from the Latin transiens, "passing over or away."