Why would a copper body help? Just a serious question?
I guess just the contact pin and spring at the bottom of copper (or any other high conductive metal) should suffice??
A copper mod would help because voltage drop would be kept at a minimum.
Therefore lets just take for example my copper nemesis @ 0.5 ohm has about a .12 drop. With a fresh sony VTC5 at 4.2, i would be getting 4.08v to my coil. Batteries will keep performing worse and worse as you vape, however because a copper mod minimizes voltage drop, if I am vaping my battery at lets say 3.8v, I would still be getting 3.68v supplied to my coil. Which, to me is still entirely vapeable. However @ 3.8v in a stainless steel mod, its going to feel like 3.2v. Which is normal for a stainless steel mod at low ohms to have a high voltage drop of 0.4-0.6 (to my experience).
even a fresh battery @ 4.2 in a stainless mod with low ohms, if it had a high voltage drop, It would already feel like your vaping @ 3.8v.
So basically if your mod has really low voltage drop, it will "feel" like it takes much longer for your battery to basically get to the point that it feels weak and needs to be recharged.
Contacts do matter as well. I recently have been trying to get copper everything just for the fact of low voltage drop. I have a few mods that are stainless steel/brass with silver plated brass contacts and they do not hold a candle to a full copper mod with copper contacts (or silver plated copper contacts). I can literally feel how much more ...... off a copper mod is when firing.
Even a hybrid adapter will minimize voltage drop even further.
Your problem could be as simple as cleaning your contacts / replacing your batteries.
Of course, im only speaking from my own experience about all this. Im sure someone might / will disagree with me. Your mileage may vary.