The blue followers are the current .40 3rd gen followers (they replaced the yellow ones).
No way to guess what's happening with
your 4056TSW without being there to inspect the pistol.
Just for the same of discussion, though, the first thing I'd check, as an armorer, would be the condition of the ejector tip and the extractor hook edge.
It's not uncommon for an ejector tip to be missing, especially if it's an older design extractor with the short tip and the sharp angle under the rear of the tip.
This image shows an older ejector (bottom) with the short tip and the sharp corner angle at the back/bottom of the tip, where it flares down into the larger body of the ejector. The top ejector is a newer revision, with a longer tip and a curved angle (reduces the potential for a stress riser to occur and snap off the tip).
During extraction/ejection, the just-fired empty cases can be grabbed by the extractor hook and pulled back to meet the ejector tip, which kicks them out of the ejection port. If the ejector tip is broken off, it's not uncommon for the empty cases to still be "ejected" as they're pulled back and hit the edge of the case mouth of the top round in the magazine. Ejection can be a bit erratic, but it can still occur.
If the ejector is broken off, though, when the mag is
empty, and there's no more "top round" waiting in the mag lips, the just-fired empty case may be pushed back and either end up sitting on top of the empty mag, or be shoved down between the mag lips.
If shoved down between the lips, it's not uncommon for there to be 1 or 2 "dents" (sort of triangular shaped) to be present on the case mouth. This happens when the loose just-fired case, if pulled from the chamber by the extractor, is hit by the rear of the barrel's tab, and/or the side of the chamber wall (mouth), which shoves the empty case backwards, and sometimes downward.
Now, if the
extractor is chipped or broken, it may not be hanging onto the case rim to pull the case to the ejector (whether or not the ejector tip is present or missing).
However ... If the extractor
spring has fallen below the recommended tension - (there's a recommended min/max tension) - then sometimes the extractor pivots, or "jumps outward" at the front, away from the case rim, sliding over it and missing hooking onto it, during the early critical moment of recoil.
I recently inspected another retired cop's well-used early production ('91) 3913. I noted his extractor tension fell almost 2lbs below the recommended minimum tension for his model/caliber. He hadn't used the gun for a long time, but said he didn't remember it exhibiting any extraction issues. The tension was too light to be within the normal factory spec, though. His extractor was also chipped/burred, so I fitted a new extractor
and put a new extractor spring in his gun.
The new extractor spring put the tension range up in the middle of the recommended range. Bench checks were good, using the gauges and tools, but more importantly, his subsequent range check using his former agency's +P loads showed the gun to feed/extract & eject flawlessly.
Bottom line, your 4056TSW really needs to be inspected by either the factory, or a gunsmith who is familiar and experienced with repairing S&W 3rd gen's.
There are standard, lighter & heavier than standard extractor springs. There are several extractor springs armorers may use to adjust any particular gun (and sometimes particular production run revision of a model) to get the tension to fall within the necessary range.
Now, the TSW's started listing 3 potential extractor springs, as therer was a standard production spring, as well as a couple of optional springs that might be needed for any particular gun. For the 4056TSW, the list I have shows there's a standard spring (unpainted), and then White and Orange springs as options. The spring tension is checked with a Wagner Force Dial gauge, used with the appropriate hooked tip for the extractor hooks, and the tool used to cost S&W armorers approx $150 to buy.
Extractors are fitted parts, which typically require filing (on an adjustment pad, NOT the hook edge), and the use of a factory provided Go/No-Go bar gauge ($70 bar gauge).
Experience with repairing the .40's is helpful, as some .40's seem to run best when the tension is higher and the extractor is tighter, and some run just fine at the other end of the spring tension and "fitment" range.
Clear as mud, right? Call S&W customer service, and hope you get a helpful representative. If not, try calling back and seeing if you get someone else.
Yes, the guns are obsolete and discontinued, and the company hasn't been replacing their 3rd gen parts inventory with any noted regularity, but they've still been repairing guns for some folks. They may have either plain stainless or black finished extractors, and springs are small and may sit around, unneeded, for years at a time.
If you have a local gunsmith who is familiar with 3rd gen's, and has the parts (approx $23 retail, maybe), and the gauges, maybe he can handle it for you. Dunno. You'd have to ask around. maybe call that guy in TX, who used to be a warranty center for S&W. He might have parts sitting in drawers, and there's been a number of people who have reported satisfactory experiences with his work.
Those thoughts are just regarding a couple of the most likely causes, though. A damaged or weakened recoil spring can also cause some head-scratching issues, as can over-powered ammo, or ammo with case rim dimensions that are on the wrong end of normal industry tolerances.
Good luck. Just some thoughts.