use this script,
// reverseArtboardsOrder.jsx
// carlos canto
// http://graphicdesign.stackexchange.com/questions/64865/is-there-a-way-to-automate-reversing-the-order-of-artboards-in-illustrator
function reverseArboardsOrder () {
var idoc = app.activeDocument;
var abs = idoc.artboards;
var abcount = abs.length;
var abNames = [];
var abRects = [];
for (i=0; i<abcount; i++) {
abNames[i] = abs[i].name;
abRects[i] = abs[i].artboardRect;
}
for (j=0, k=abcount-1; j<abcount; j++, k--) {
var abRect = abRects[k];
idoc.artboards.remove(k);
var newab = idoc.artboards.add(abRect);
newab.name = abNames[k];
}
idoc.rearrangeArtboards();
}
reverseArboardsOrder();