After getting no help from Medion at all, I have stumbled on the answer by accident. When the manual says touch and hold the button until it switches off, what it really means is touch and hold the button until it starts the 3..2..1 countdown, and let go as soon as it starts counting down. Initially I was keeping my finger on the button until it shut down, at which point it wakes up again. By removing my finger at 3, it does indeed shut down.
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