Cannot move a node

I'm using the Shape to move nodes of straight-lined drawings.

Think of a line that is supposed to be horizontal but appears to be a few pixels (mms) off.

But I have noticed that for some lines the Shape tool does not seem to work anymore. I.e. I can select a node and move it but as soon as I release the mouse button the node flips back to its original position.

These lines originate from copies of earlier drawings and have undergone any number of rotation and / or mirror transformations. Apparently, this has also caused the deviations in the position of the nodes, that I am unable to correct now.

For new lines though, the Shape tool works correctly...

What am I missing?