Given these are 40 years old one might expect a bit of problem.
Once per mag the 59 leaves a loose case in the port lying length ways on top of the mag and of course stops the slide.
It does this with factory mags with good springs, new Mec-Gar mags and other mags.
The extractor looks fine with no chips or damage. It has plenty of tension. It will hold a live round under the extractor while shaking the slide (old 1911 test).

The jam occurs mid magazine (about the seventh to tenth round).
Ammo is Federal 115 or 124 or Rem 115 FMJ.

I cannot understand what is causing this.

Try replacing your recoil spring. They are available from Wolff Gunsprings. It may be time for magazine springs also.
I know you dont want to hear this but it may being caused by a weak extractor spring. On those Smith 9`s, its best handled by a gunsmith that knows them.
Last, but not least, maybe it is starting to get fussy about ammo.
Your gun was made when most standard 9mm ran a little hotter than it does today.
Good Luck.
Jim

My 6906 did this one time today.
It pulled the empty out of the chamber and it was laying on top of the next round from the mag.
Mag wouldn't come out, because the top round in the mag had slid forward as it tried to feed it into the chamber, but was unable.

It did it once in the three mags I fired.
First step will be a thorough cleaning.
But, it may be as simple as a round that just didn't have quite enough oomph.
Dunno.

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What would Jim Cirillo do?

With the price of smokeless powder these days, I can see ammo manufacturers reducing the amount of powder in each cartridge by just a fraction of a grain. When you make a production run of a million rounds of ammo, those fractions of a grain reduction in propellant will add up to big numbers and to the corporate bean counters, they are doing the happy dance.

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Bill

I have had this same issue on a high round count Glock 17 (30K).

Installed a complete slide rebuild kit
Installed an extra OEM barrel from a new Glock (installed a Wilson barrel so OEM barrel was lying around)

500 rds so far and no issues, however, only target 124gr Aguilar ammo has been used.
My vote would go for: Dirty or bad extractor, bad recoil spring, or bad/worn extractor spring.

Interesting tid bit about "guns last your lifetime". I'm prepping for the military SAMI course and had to take an online course for the M500 mossberg shotgun. According to them, the stated life expectancy of this tank is....10K rounds. Long story short, springs go bad, barrels definitely get shot out, and from my experience, recoils springs should be changed around the 5K mark.

Replacing the recoil spring with a new, OEM spring is good advice.

If you haven't already done so, check the integrity of the extractor hook (with a magnifier), verify the tension of the extractor spring, and that the extractor moves freely in the slot.

You might also take a look at the ejector mag depressor lever, and spring. The levers are prone to damage. If your ejector is bent or broken let me know I can send you a new one. The newer design is less likely to break. The older design has a "squared" profile under the nose....the new ones are curved, and consequently, are far more durable.

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Ret. LE, FA Instr, S&W Armorer