A speaker lies awake, eyes open, unable to sleep because of the pain inside them. The poem is quiet and sparse, and that suits the mood: the long, restless stillness of a night when nothing helps. The aches feel like something that can't be swapped out or fixed ("that I can't replace").
The second half sets up a contrast. The speaker has good feelings, but they drift away quickly, while the hurt stays put. The last lines are a little tangled, and that seems fitting. Reading them, I take the speaker to be saying that even though the pain is useless, it lingers anyway. Nothing is gained from it, yet it won't leave.
The title, "stay," works in two ways. It names what the hurt does, and it might also be a quiet wish for the good things to hang around. The overall feeling is tired, heavy, and honest, without any dramatic outburst.