What is the ruling on one who disregards the statement, "I ask you by Allah not to do that," and is an expiation for a broken oath obligatory upon the speaker?

The statement of a person, "I ask you by God not to do such and such," is not an oath, so there is no expiation for it if their request is not met. It is recommended for the one who is asked by God to answer the asker, out of reverence for God, unless their request is without right or would put the one being asked in an awkward position.