This thread in the Nikon_F group on Flickr gives some illumination. One poster reckons the problem is "the ring resistor which is of a design that if cracked or worn thru stops functioning". Naturally, he gives no source for that, but maybe it's this page on the somewhat eccentric Michael Liu F site, where he says the "universally reviled" ring resistor informs the meter of the aperture, and that it "is irreplaceable if it gets dirty (and scratched) or cracked.".
Although the meter is/was a very good one, it wouldn't be the end of the world if it wasn't working. It's aesthetically dubious, and anyway using a meter is overrated. No doubt a meterless (or eye-level) finder (or prism), can be gotten in due course. That's part of the point of getting an F, the modularity.