Based on the description of the problem it looks like some time after the units are turned off the AMT configuration is reset, perhaps the IP addresses are flushed in the units in question or the NUCs lose power completely.
Can you enter the AMT console of the NUCs in question using a regular browser from Windows? Even if they are off, you should be able to access the web console of the AMT and turn on the system from there.
Do you see the units in the network while they are off? I am not sure if VNC Viewer does but there some Intel® vPro™ Technology tools that let you scan the network to identify the AMT ready and configured units, this way you can create a check list. The units show up even if they are turned off. Visit the following link to get more information about Intel® Setup and Configuration Software: https://communities.intel.com/community/itpeernetwork/vproexpert
The minimum requirement to have access remotely to an AMT based system while it is off (S5 – os shut down) is to make sure the unit is connected to the power source. Besides that the use you give to it depends on the provisioning you deploy.
You can try waking up those systems with a magic package instead of using the AMT just to compare and to make sure they are receiving power.
You can also swap the AC adapter of the working unit with any of the other three to see if the problem has to do with power.
If these recommendations don’t help you can get support for Intel® Active Management Technology and Intel® vPro™ Technology directly from our engineers by visiting the following web site:
Please be aware that support for this platform is provided via web only through the previous link.
If you consider that this problem has to do with a defect and the units are under warranty you can also contact our Customer Support channels for warranty assistance. Visit the following link; choose your area and product and then the support channel you prefer: