Your issue sounds like a connection problem. I think you're probably overtightening the leads initially. If you have too much pressure on them when you pulse, the wire flattens too much and there's no going back. There's nothing substantial enough in there for the posts to bite down on anymore, so the screws keep coming up. And the more you re-tighten, the more compromised the connection becomes. The wire becomes brittle and the heat/pressure starts eating it every time you move it/adjust the screws again. At that point, the only fix is to completely back out the posts, choke up on the leads, and set the screw on a new point in the lead.
Be gentle when you're first fixing your coils. Wrap and mount them in a way where you don't have to tug/wiggle much, if it all. Use low wattage for your pulses, too. The goal is to get good enough at it that a little squeeze and tilt is enough. Use the rod to position them as close to where they need to be before your fist pulse. Minimal tension. If you can do this, then you don't need to tighten the wire much at first. Starting off, leave about 3mm hanging out of the back of the posts. Once you tighten, very carefully wiggle the coils and watch those pieces hanging out. You want to tighten them *just* enough that those don't move. You'll feel like you can tighten more. Don't. After pulsing a few times, the screws will back out. Tighten them back to that tension and they should settle into that position. With thicker wire, you may have to do this several times. Just remember, small increments.
The idea here is that when you first start heating the metal, it is expanding and it needs room to do so. After enough heat is applied, it hardens. If you clamp down too much while it's still soft, the wire will give out. Once the metal hardens a bit, it tends to stay more secure and expand a lot less.