"Kalechn"
Mystery solved!

Philologos is "tickled" at the Satmar succession dispute. There's no accounting for taste, though I find this a strange source of humor. At any rate, his latest column talks about a word which the late rebbe is said to have used with his son:

"You think I'm already kaleching?" Rabbi Moses was also quoted by New York magazine as having said to Aaron on the same occasion. (In Yiddish, presumably, this was "Du maynst az ikh kalekh shoyn?") "Kaleching," we are told by the article, means "mentally declining," although I suppose that "senile" would be a bit more colloquial.

Philologos further speculates:

With Slavic, we do a bit better. There is a Slavic verb — kaleczyc in Polish, kalitset in Ukrainian — that means to cripple or disable. This verb gives us the Ukrainian noun kalika, "a cripple," which has the same meaning in Yiddish. "Disabled" and "mentally declining" don't seem too far apart. Can this be the source of kalekhn?

It's not very likely. Apart from the fact that the Slavic verb is transitive and kalekhn is not, there is no phonetic reason that the Slavic "k" should have turned into a Yiddish "kh." I can't think of other Slavic words with which this happens.

The columnist goes farther and farther afield until he hits upon an implausible Talmudic derivation. Much more likely, I think, is that the transliteration "ch" in New York magazine is meant to represent the Yiddish sound "tsh" (טש), and that the Yiddish word meant is, in fact, kalyetshen (קאַליעטשען), a well-known verb meaning "cripple, disable." No need for etymological creativity here.

Update: I'm wrong again! I've learned a new word: (far)kal(e)kht, פֿאַרקאַלעכט, meaning senile, from the Yiddish kal(e)kh, קאַלעך, lime or plaster. See the comments for more. Yet another example of the differences between "my" Yiddish and "theirs."