Is it just the arm that is loose on the tapered stud, if so you could fit some thin slivers of soft metal between the shaft and the stud, and when you tighten the nut, the soft metal "should" compress enough to give a good grip.
I guess you have been trying to clear snow and ice off the screen:doh:doh
thin copper or maybe even shim steel might work.
Scrape out the splines on the shaft and the wiper arm, as the arm might have been stripped.
best regards,
Rustic
EDIT...
You could always drill through the wiper arm, then the stud and put in a pin, or nut and bolt..
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