Considering the age of the gun, it wouldn't be a surprise if the extractor spring was worn and weakened, allowing the extractor to slip off the case rim because of how recoil forces act on the extractor & its spring.
It also wouldn't be surprising if the extractor hook was chipped or broken. We started to have to replace an increasing number of chipped/broken extractors and weakened springs in our aging inventory of 59XX guns dating from the same production period ('89/90) once they reached the 12-16 year point in-service.
The extractor in your early production 5906 is a bit different in the shape of the hook, and the area directly behind the hook, than what's being used nowadays.
Here's a couple images to allow you to see how the extractor hook normally appears (including a bevel at the bottom of the hook). The larger extractor is for a .45 and the narrower one is for the 9mm.
BTW, the machining of the slide's extractor recess and the extractor spring hole were done on equipment operated by hand back in those days, so sometimes there could be some variation of tolerances. This is important because for the older 59XX series guns S&W made a couple of revised extractor spring sets for repair use. Sometimes the stock spring wouldn't provide the appropriate tension for normal function and a different spring (and sometimes even a nested set of springs - now obsolete for repair use) would be needed. Sometimes the bottom of the spring's hole wasn't machined quite correctly and a small ball end mill would be needed to reshape it so the repair spring would sit in the hole properly.
My point is that this is one of those repairs where the right diagnosis is important, meaning the folks at S&W would be my first thought for examination and repair. They might even make any other repairs, or replace some older parts with newer revisions (like the ejector), too.
Replacement of the extractor itself requires the use of a force dial gauge, a Go/No-Go gauge and some experience in filing/fitting the new extractor, too.