Delta Unisaw

First thing I would suspect is the washer next to the nut. It's cup shaped to apply pressure against the machined surface of the arbor washer. Perhaps the cup has become flattened and no longer has any spring to it.

That sounds right. I'd replace the nut while I was at it; after 30 years it doesn't owe you anything.
Now, finding new ones, that's a project.

What Andy said sounds right. I'd replace the nut as well.

Here's an old discussion on the subject...
Replacing 5/8" arbor nut for my table saw - by Michael Kramer @ LumberJocks.com ~ woodworking community

Try screwing the nut on the spindle part way and wiggle it and see if there is excessive play. The threads could be worn in one or both. I just had this thought.

If the arbor stops faster than the blade centrifugal force wants to, it will loosen the blade. Are your motor and arbor bearings in good condition? If it doesn't coast to a stop it may be loosening the nut.

I once designed an electronic brake for an older table saw. Applying DC to an induction motor will stop it from coasting after the AC power is removed. My brake initially worked too good, and unscrewed the arbor nut. I had to reduce the DC braking voltage to just slow the motor rapidly and not stop it suddenly. If it stopped too suddenly the blade would try to keep going and it would loosen the arbor nut no matter how tight that I tried to make it.

Charley

I've had good luck finding replacement parts here: ereplacementparts.com

Saw Center in MA has both the flange and the right and left tilt arbor nuts for for approximately us$30.00.


422-04-103-5001S -- Outside Blade Flange

902-01-200-9848S -- Blade Retaining Nut for Right Tilt

902-01-201-2571 -- Blade Nut for Left Tilt saws

Besides parts, Saw center will also rebuild the arbor if needed. Bought hard to find parts from them when I had a Uni-saw.

http://www.sawcenter.com/unisawparts.htm