So the project is definitely saved within Unity before opening the new script in MonoDevelop?
Seems quite odd behaviour, but of course it’s a very old version of Unity and Windows 10 wasn’t around then.
There are a number of things which could be factors and trying to work through all of them will probably just have you going around in circles.
You could try installing a newer version of Unity, later in the course you upgrade to version 5.x anyway, and to be honest there isn’t really much reason not to just use 2017. There are some API differences but these are documented in the course and also on the forum.
You can install multiple version of Unity, as you are on Windows you will be given an option to specify the install location, so for example you could try Unity 5.6.5 and install to \Unity 5.6.5, this would keep it completely separate from the older version - you could then repeat the test.
Another thought is that MonoDevelop is quite inferior to Visual Studio and there really isn’t any reason not to use Visual Studio, especially as you know that actually does work. It is much more feature rich than MonoDevelop, a lot of people switch as they progress anyway.
Fathoming this one out I think may depend on how much time you want to spend on trying to get an old version of Unity to work with an inferior text editor, to save in a less than ideal location on your computer
Updated Tue Apr 17 2018 00:14
Just another thought… do you happen to have anything else open which could be using that file, more than one copy of MonoDevelop for example, or anything else? Or even multiple times within the one instance of MonoDevelop, e.g. same file two tabs?