Some simple resolutions would be: a freak lightning strike disables the robot's button-pressing hardware. Or a cosmic ray flips a bit in its machine code, causing it to shut down. Or the robot's designer suffers a heart attack before turning it on.

These may seem like contrived examples, but when you eliminate all outcomes that aren't self-consistent, it may be that _all_ the remaining possibilities are contrived. Probability gets weird when time travel is involved.