First, you get the error because you are using a text editor for this. This means that every time you open the file, edit and save it, the original is overwritten with the new contents. Whether you added a single line to the end or 100 lines all over the place is irrelevant, the point is that the file is being opened, edited and saved and that overwrites the contents.

For example, compare your workflow to running this:

for((i=0;i<20;i++)); do echo $i >> file.txt; sleep 1; done

That will write a number to file.txt every second for twenty seconds. If you open another terminal and run tail -fn 0 file.txt, you will see the output you expect.

So, to get the desired behavior add the text to the file using >> from a terminal instead of manually editing it.

More details

nano seems to be the odd one out here. Most editors when opening a file then saving it will actually delete the original file and save a new one with the same name. You can test this by checking the inode number of the file:

$ ls -il file.txt

16647801 -rw-r--r-- 1 terdon terdon 9 Apr  6 18:19 file.txt

Files are simply hardlinks to specific inodes, in this case, file.txt points to inode 16647801. Now, open the file in gedit, add a line and check the inode again:

$ gedit file.txt

$ ls -il file.txt

16647854 -rw-r--r-- 1 terdon terdon 13 Apr  6 18:23 file.txt

As you see, the inode number has changed, in other words, the original file was removed and a new one was created. nano does not do that, trying the same thing with nano does not change the inode. It does, however, delete the original contents overwriting them with the new contents. That's why tail actually shows the output, if you try it and edit the file with gedit (or emacs or a number of other editors), the extra lines you add won't be shown in the output of tail at all.