I don't think that would make much of a difference because then it still can answer conditional on what its answer would be when it is asked the same question again the next day, which would presumably be the same answer unless it got new information during that wait period.

A perhaps safer but less efficient alternative is to design a Predictor (without keeping any backup copies of its source code), such that with some small probability, it will delete its source code and shut down instead of answering your question. Then if you still want to know the answer, you have to design a new Predictor with the same specifications but a different algorithm. The Predictor's answer (if it gives one) refers to what would happen conditional on it shuts down.