(state after opening the previously saved design - no idea if that is crucial)
Don't understand this behavior:
In the screen-shot you see "path351" which is referenced in "textPath175" ("text175" produces the fake wire-wrapping).
"path351" is obviously bent (which is the intended LPE-effect) but when selecting it, only the original, unaffected path pretends to be accessible for the Node-Tool.
(Contrary to editing the path-data-attribute (d="…") in the XML (which corresponds to the bent object), editing the (rectangle-shaped) original with the Node-Tool has no effect.)
Attributes referring to the LPE and the def of the LPE itself are not shown in the XML-editor.  

p.s.: one of the riddles solved.
The XML-editor hides crucial parts of the svg-code from the user.
Opening it in a text editor reveals several attributes of that path which are invisible in Inkscape's ui. Especially the 'inkscape:original-d'-attribute is what makes the path inaccessible for the Node-Tool.
… which renders the XML-editor flaky.

How the (other) LPE-attributes and the def of the LPE got lost remains Inkscape's secret. … for now - hopefully!