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?
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Yes, since the spelling reform, "auf dem Laufenden" is capitalized:
The IDS rule (pages 61-52) actually contains that example:
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
but (a rather contrieved example, a flea sitting on a runner)
It must be "auf dem Laufenden", according to this Duden rule.
Note the m in "dem".