I would say for most people a long rest stops concentration, since unconsciousness causes incapacitation and that is listed as something that breaks concentration. Now some races like elves with trance and more than likely warforged could keep up concentration while taking a long rest.
Short rests would not stop concentration for anyone.
Another vote for not on a long rest. And I'd say that goes for Elves, too. They may not need to sleep but they need to enter into a trance and I think that requirement rules out concentrating on a spell.
I agree. Trance is described as a form of deep meditation. I don't see how one could do that and still maintain their concentration on something else.
Fwiw, you don't need to be unconscious to be incapacitated in 5E. Based on the description of the Elven Trance in the book, I'd consider an elf in trance to be incapacitated, much like a stunned creature. They're not fully conscious (definition of semi-conscious), nor fully aware of their surroundings, often dreaming. Elves may have developed a hyperefficient variant on sleeping, but that doesn't mean they're at full capacity.
Not that I'm sure it really matters, but there's no reason to make an exception where one's unneeded.
It's certainly possible to rule that way, but since they are unaware of their surroundings in their trance, they would be unable to take reactions or actions (interesting that surprised and incapacitated have near identical results in this edition), so a shield spell would be tougher.But to me an elf in trance could take a reaction
Huh, I would rule you can concentrate and rest. You can fight and concentrate, resting should be easy compared to that. Sleep? No.