It's the glitch where you freeze in vats with certain weapons. You stand there in an awkward position while your enemy slowly shoots you to death. This happens with the lever action shotgun, Hunting Shotgun, Cowboy repeater and sometimes the brush gun. I have all the patches so I know that's not the reason. Does anybody know what I'm talking about?

Maybe they can't?

The last http://fallout.wikia.com/wiki/Fallout:_New_Vegas_patch_1.4.0.514 they released fixed over 120 things so I find it hard to believe they can't fix one thing. I can understand if they overlooked small things but this ruins combat and makes cowboy weapons unplayable.

They tried. On every single patch.
They couldn't figure it out before production ended. Every time they patched and said it SHOULD be fixed, but every time it just transferred the glitch to somewhere else.
For example, I can tell you why you're having it. You're going into VATS directly after reloading a pump-action and/or lever-action gun right after reloading. If you reload while crouching, it won't happen. It used to be the other way around: reloading while crouching caused the glitch whereas reloading while standing worked fine.
It also seems more prominent when you take the Rapid Reload perk.
You can also usually visually see or feel if you currently have the glitch "on you" by going into third-person. Lever-action rifles like the Brush Gun and Cowboy repeater, the lever may be sticking out if you go into third person, or you'll see a random metal bar sticking out of the back of the gun. Guns like the Holorifle, the chamber for sticking the Microfusion cells in will be wide open. Revolvers with either show the chamber randomly floating behind the gun itself (.44 magnum) OR the gun won't be sitting right on your character, either at a weird angle or INSIDE your character. (.357 magnum, Lucky) You can feel the glitch in that when you attempt to fire (not in VATS) there will either be a delay in your first shot (slight, so that it feels like the first shot does nothing but the second fires two shots) or you'll randomly fly a foot or two backwards/sideways upon firing the weapon. Sometimes you don't even have to fire the weapon, but rather your character just feels like he's flung backwards/sideways after the reload or the animation for cocking the gun plays twice.
If either of these occur (visually glitched or you can feel it), you can fix it by re-equipping or holstering-unholstering the gun, THEN continuing.

If you pay attention to signs like that, you can easily learn how to work around it. Like I said though, they DID try, but couldn't figure it out. The result being that one patch it's prominent with Rapid Reload, the next it's prominent while crouching, the next it's prominent while standing, the next it's prominent after reloading etc...Somehow the bug only managed to get moved around, but never fixed.

Thanks for letting me know how to get around that annoying glitch. However, I don't think it will be a problem anytime soon because I ditched the lever action shotgun for the riot shotgun. I really wish it was some way they could patch this but this was their first time using the gamebyro engine so I'll give them the benefit of the doubt.

The lever action shotgun glitch still exists out of vats as well. I agree with the OP that these issues should have been fixed a long time ago.