Three short lines, and a small scene: people are trying to celebrate New Year's with a drink, and the rain cuts in. The word "again" is the key. It tells us this isn't a one-off annoyance. The rain has interrupted before, and the speaker half expected it.
The title, "No change," fits that feeling. New Year's is supposed to mark a fresh start, a moment when things might be different. Instead the weather carries on exactly as it has been. The poem doesn't complain loudly, though. The tone is dry and a little amused, the shrug of someone who isn't surprised anymore.
The mood is quiet and wry, with a hint of weariness. Judging by the wording, the speaker is probably outdoors or at least near the weather, and the toast gets pushed aside. The poem leaves it there, without explaining what the rain means, so we're free to read it as a gentle joke about resolutions that never quite take hold.