One of the meanings of “repeat” is to say/write again. Does this mean it is wrong to say “repeat again” in a sentence?
If the answer is yes, then please explain the following sentence given on p.1,284 of the Oxford Advanced Learner’s Dictionary (7th edition) under the definition of “repeat”: She kept repeating his name softly over and over again.
Yes, we don’t usually say or write “repeat again”, because it would be redundant to do so. In the case of the sentence from the OALD, the idea of repetition is expressed three times: in the word “kept” (= did something repeatedly), in the word “repeating” and in the idiomatic phrase “over and over again” (= many times; repeatedly). Perhaps “She uttered his name softly over and over again.” would get rid of the redundancy, without losing the literary effect of the original.
Just because something is in print does not mean it cannot be questioned, and I am glad that you questioned the logic of that sentence.