Over and over, the speaker writes the same letter: "I wrote you an apology letter." The repetition makes it feel like someone circling a regret they can't put down. At first the letter goes nowhere useful. It is sent to the speaker's own self, reread late at night, or clenched in a fist because courage runs out. Then there is a second letter, addressed to the speaker, apologising for having to leave, though the mind "wouldn't agree." That suggests the speaker is still divided about the decision, even while saying sorry for it.
In the last stanza the letter finally gets sent, and the answer is painful. It comes back two days later, and the other person's mind is already made up. The mood is quiet, guilty and sleepless, shifting to a flat, heavy disappointment. The poem seems to say that an apology offered too late, or only after much hesitation, may no longer be wanted.