Frost's allusion to the Garden of Eden story is meant to remind us that the idea that nothing lasts forever isn't a new one; it goes right back to the very dawn of civilization. We might like to think that certain things in our lives are perfect. But Frost wants to shake us out of our complacency. If even the Garden of Eden—this beautiful, God-given paradise, perfect in every way, shape, and form—could sink to grief, then what hope is there for us and the things we value most?

Nature is often seen as a place of retreat, a haven of peace and repose. But since that fateful day when Adam and Eve defied God by eating of the Tree of Knowledge, nature as well as humanity has been subject to decay. As nature and humanity are in lock-step in their fallenness, all we can do is acknowledge the numerous imperfections in ourselves and the world in which we live.

Frost alludes to the story of the Garden of Eden in "Nothing Gold Can Stay."  This allusion comes up in the second half of the poem when he says

So leaf subsides to leaf/ so Eden sank to grief/ So dawn goes down to day/ Nothing gold can stay.

With this line, Frost adds a new dimension to his poem.  While most of the poem, literally, is about the changes that occur in nature and the fact that colors and new growth don't last, this reference to Eden brings to mind the loss of innocence that occurred after Adam and Eve broke God's commandment by eating the apple and, as a result, were cursed and cast out of the garden.  In this way, "Eden sank to grief."

Since Frost rather matter-of-factly inserts this line into his poem, he does not seem to be questioning the myth here.  He seems to just be saying, this is the way it is.  It's hard to know from this short passage exactly what his thoughts were on the whole Creation/Coming of Evil story, but he seems to be saying in this poem that nothing good lasts forever; innocence is lost, colors change, the sun sets, living plants and creatures die, seasons come and go - it's all part of the cycle of life.