Script to save, close, reopen, and continue ("Error 8702: there is no document")

Hi all,

I'm trying to create a script which will allow me to save an Illustrator file, close it, reopen it, and continue working on it (in this case, add a layer). I've tried a number of different methods, but each one gives me an error ("8702: there is no document"). I'm guessing this is due to the document variable being reset once the document is reopened? I've tried a few different things, but can't seem to crack it:

Firstly I tried running it as a single function--

var doc = app.activeDocument
var docPath = app.activeDocument.fullName

app.executeMenuCommand("save");
app.executeMenuCommand("close");
app.open(new File(docPath));

var newLayer = doc.layers.add();
  newLayer.name = "New";

Then I tried breaking it into seperate fucntions, with the variable redefined--

saveCloseReopen();
addLayer();

function saveCloseReopen(){
  var doc = app.activeDocument
  var docPath = app.activeDocument.fullName

  app.executeMenuCommand("save");
  app.executeMenuCommand("close");
  app.open(new File(docPath));
}

function addLayer(){
  var doc = app.activeDocument
  var newLayer = doc.layers.add();
    newLayer.name = "New";
}

I tried using app.documents[0] instead of activeDocument to define the variable; I tried running app.activeDocument = doc after reopening, which I've had work in a similar Photoshop script. I've even tried writing each function as a seperate script, and calling them individually using $.evalFile -- I was really surprised this didn't work, but I'm still getting the error. 

Any advice massively appreciated, I'm ready to pull my hair out at this point!!

Thanks in advance.