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dco
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Appart of the terms "short rest" and "long rest" there is a wall of text in that section of the book where the "rest" word is used.Except that "short rest", "long rest", and "concentration" are all game terms with their own unique D&D definition that has nothing to do with the common english language definition.
Concentration only has a few key things that stop it.
- Death
- Taking damage
- Being incapacitated, unconsciousness causes this
- Casting another concentration spell
- Failing a Con save under certain environmental phenomena
Resting is not listed as one of the things, so a short rest doesn't stop it plain and simple. If you go unconscious and therefore incapacitated during a long rest that would stop concentration as well.