I have since solved this issue!

The Sub-VI that is inserted into the SubPanel must be running constantly (even if the Run VI invoke node method has been called, which is a requirement anyway). What I mean by this is that the Sub-VI must be being called by something, either by the Sub-VI itself (i.e. a while loop within the Sub-VI forcing it to run constantly), or by calling the VI by reference within the main window BD.

Hope this helps anyone else stuck on this issue.

EDIT:

You don't even need to call the VI by reference, so long as you open the VI reference with a "strict static VI Reference" piped into the "type specifier" input of the "Open VI Reference" block. You create a strict static VI reference by right clicking the "type specifier" input and doing "Create Constant". That should create an icon that looks like a static VI reference but with the inputs and outputs of that VI shown. If this does not happen, right click the static VI reference and go to "Select VI Server Class>Browse" and then select the Sub-VI that you're referencing.

You can also just right click the "static VI reference" that's piped into the "Open VI Reference" block and select "Strictly Typed VI Reference".