Apparently the fired case is hanging up on the case mouth of the following round.  this is more pronounced with Russki Brown Bear steel cased ammo, but it intermittently occurs with brass cased ammo.  I have a new extractor on the way - the existing one has a burr at the hook - but I am leaving no stone unturned.  Any suggestions? Ops

Waiting for the extractor would be a good time to polish the chamber...how does it look?
Not familiar with the Argentine HP, does the extractor use a spring, like most copies?
If so, that's a cheap item to try too.

Polished chamber, slide bottom, etc and found the corner burred over on the extractor, I reshaped it with a file and added an AR extractor insert, now it works.  Also have a Cylinder & Slide hardened extractor and spring on order. Apparently this is a weak spot on HiPower clones, so I have another stock extractor on backorder at Numrich.  Evidently some of the 'foriegn' P35s did not get heat treated properly.  Ops

I had a raft of problems with my FM Argentine High Power.  I finally gave up on it and traded it.

There is a vocal contigent of Argentine HP fans who say that they are the equal of the Browning guns, but from what I have seen I have to disagree.  

I also replaced the stock recoil spring with an 18.5 lb Wolff spring for  light 40 Short & Weak loads.  Once in a while I bet a fail to full cock if I limp wrist it.  Otherwise, its still the most accurate 9 I have ever shot, and I think it will become one of my favorite pistols.  Ops

Ken,

 Have to agree with you there. The early FM hi powers weren't bad... Basically just their military models without the extra stamping on the slide. The newer Detective models though aren't that great. Have one in right now for work, trigger has about 3 days worth of takeup.. Customer doesn't like it. Go figure. The old Military FMHPs are not bad though

Don't overlook the magazine.  Browning factory and FN military contract are best.  Different follower designs, springs, and shapes of the front ledge of the magazine underneath the bullet of the top round can interact to cause FTFe/FTEj.
Since you describe the problem as the fired case hanging up on the case mouth of the round to be, it's possible your mags are hodling the rounds nose high.  I had a problem somewhat similar to this out of my Israeli MKIII while testing an Inglis mag I'd bought.

XH1927