The antonyms for "keeping upon" can vary depending on the context in which it is used. In the sense of "keeping upon a task," antonyms could include procrastinating, avoiding, neglecting or abandoning the task. In the sense of "keeping upon a topic," antonyms could include diverging, switching, veering or digressing from the topic. In general, antonyms for "keeping upon" can imply a lack of focus, attention, or interest in whatever it is that is being kept upon. Therefore, the opposite of "keeping upon" in most cases would be to stray away or break away from a topic or task.