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The analog signal is converted to discrete signal. Even after the conversion, the frequency of the actual signal still remains the same. If the frequency of the discrete signal is different from the analog signal, the reconstructed signal would be different again. This is not what we expect.

So base spectrum for similar signals have same frequencies, whether they are discrete or analog.

Why do the repetitions occur?

The original analog signal is multiplied with a dirac pattern. The base frequency is then shifted to the places, where diracs are available. So long the diracs keep repeating, the base frequency do repeats.

Hope you are convinced with my answer

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Q: Why is the frequency spectrum of a discrete signal repetitions of the spectrum of the analog signal?
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