Looking in linguee.de, I've found just about as many versions with "Laufenden" as with "laufenden". Is this perhaps something that has changed in the new spelling reform?
Yes, since the spelling reform, "auf dem Laufenden" is capitalized:
Wörter anderer Wortarten schreibt man groß, wenn sie als Substantive gebraucht werden (= Substantivierungen).
The IDS rule (pages 61-52) actually contains that example:
Die Direktorin war auf dem Laufenden.
Yes, this has changed with the spelling reform: according to canoo, it was laufenden before and Laufenden after the reform. Quite generally, capitalization has been simplified with the spelling reform – as a rule of thumb, you use a capital letter whenever the word is nominalized. Here the article dem shows us that it is auf dem Laufenden.
The old spelling was more complicated, but it allowed subtle differences: adjectives were often not capitalized when used in the figurative sense. So before the reform it was
Ich bleibe auf dem laufenden.
but (a rather contrieved example, a flea sitting on a runner)
Der Floh bleibt auf dem Laufenden.
It must be "auf dem Laufenden", according to this Duden rule.
Note the m in "dem".