Why? I have discovered the reason why only recently, so I might as well share it here. Well, it's one of the reasons or one of the possible scenarios.
First of all, I only started using the Hex Editor plugin for Notepad++ only recently. So I was not aware that Notepad++ had stability issues with this plugin. But it figures! The plugin has not been updated for a very long time (try six years), while Notepad++ has been updated regularly (a dozen in a year). At some point, Notepad++ became incompatible with this plugin.
It's not a major issue the way I see it. But I can understand why the author of Notepad++ wants to move past this plugin and disable it each time Notepad++ is updated to a new version. The installer script moves the plugin to a subfolder named "disabled".
I had some NFO files on my computer recently, and when I right clicked on one of the files and chose to edit it in Notepad++ from the context menu, Notepad++ crashed. I thought that was weird. So I started Notepad++ and then dragged and dropped the file onto it and it worked. So it crashed each time I used the context menu to open the file, and it worked each time I dragged and dropped the file or used the open file dialog.
A few weeks later I got the prompt telling me that a new version of Notepad++ is available. So I downloaded and installed it. This is the first time I got the message telling me that the Hex Editor plugin was unstable and had to be moved to the "disabled" folder.

I had a thought that this might be what had been causing the crashes. As it turned out, it was! Right now I am using version 6.9.2 of Notepad++ and 0.9.5 of Hex Editor plugin on Windows 10 version 1511 (10586.494). As soon as I move the DLL file for the Hex Editor to the plugins folder to enable it, and then use the context menu to open a file, it crashes the program. If I shut it down, move the DLL file back to the disabled folder, then it does not crash when using the context menu.

Note! This only happens if the file name extension is NFO! So for a file with the name extension of TXT is not affected. I have not tested a lot of the other file name extensions I have on my computer, but I did test a few of them (e.g. JPG) and it appears as if only files with NFO extensions are affected.
In case someone finds this interesting, here is what to do to replicate it.
- Install Notepad++ version 6.9.2.
- Install Hex Editor plugin version 0.9.5.
- Create a new dummy file on the Desktop named dummy.nfo.
- Right click on the file and choose Edit with Notepad++.
Note that some older versions of Notepad++ will trigger the bug as well. I don't know what version introduced this issue. But if you use a too old version then the error will not appear.