From what you have related, I am thinking that the most likely cause would be a power adapter that is starting to fail. Do you have a second one that you can try? If not, contact Intel Customer Support. They may be able to provide you with a replacement at no additional cost to you...
Thank you for your answer. This morning, the NUC doesn't start
I don't have another power adapter no. I bought the one I have separately of the NUC and I don't think I can tell the after sales services to change it.
Do you know if another power adapter could work? Regarding how long it worked, I would like to try another one, if possible.
You can use any adapter that meets the correct voltage (i.e. 12V) and the minimum amperage/wattage (3A/35W) and has the correct tip for plugging into the NUC. By 'minimum amperage/wattage', I mean that, while they do not recommend it, you could use an adapter that can deliver a higher amperage/wattage, so long at it outputs at the correct voltage (i.e. 12V).