I'm guessing that the serrations on the pivot post and/or the arm have worn to the point where the arm isn't securely attached anymore, despite the nut being tight (which I assume you have already checked, and assuming also your wiper arm attachment is the same as on my 380SE).
I have been able to fix such a situation by applying a coat of JB Weld to the pivot post, a smear of grease on the hole on the arm (so the arm doesn't get bonded to the post), then re-attach. The JB Weld will find its way into the worn serrations and provide enough friction when set-up to hold the arm when the nut is tightened.
You're probably looking at a new arm and maybe a new post/linkage piece for a proper repair.....

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1986 560SL
2002 Toyota Camry
1993 Lexus