I have been fighting this problem with a 650 for about 15 years. In my opinion, the design of the 650 was not one of Dillon's finest moments, perhaps why it has apparently been discontinued. Anyone who has owned one can attest to having "650 finger", which is where you have your finger trying to push the case into position while you also are pushing ram up. I know that seems kind of stupid on my part, but at least I am not the only one. Hurts kind of the way hitting your thumb with a hammer does, and it will eventually stop bleeding.
Additionally, the kind of advice and help you will get from Dillon when you call them depends on the person you talk to and the mood that he (never gotten a she on the phone) is in. I have had some great help and some real crappy help. Now, before anybody gets upset with me about all of that, let me also say that NO ONE stands behind their products better than Dillon. Not too long ago, I got authorization from them to send back my very tired 650. About 10 days later, I received a new one. Didn't even pay shipping. I have also reloaded about 200k rounds or more on my Super 1050 and have never had a problem that was not of my own creation.
I have found a couple of things to be helpful, but not foolproof. First, as someone mentioned, make sure the mechanism that pushes the case into station one pushes it just the right amount. Too much travel and it wants to bounce out, not enough is not enough. Also, as mentioned, keep the face of that clean. Two, make sure the grooves in your shell plate that hold the case are clean, I use a dental pick to clean those out periodically. Third, get some heavy grease and put a fair amount in between the ramp (under it) and the body of the machine. Replace this as needed, because it will disappear. This dampens the vibration when the shell plate snaps into position. Four, keep the shell plate as tight as possible to the frame without it binding, and if your ball bearing that indexes it is too snappy, consider cutting the spring a little. I have also found that the faster you try to cycle the machine, the more of this "bouncing" occurs, and smoother and slightly slower cycling helps. It is also helpful to have that thing firmly anchored to a really solid bench.
Lastly, and this is probably going to give you the best results, use a sizing die that has a generous radius on the bottom. I was using a Lee sizing die in .40 caliber because it's design would size the case further down than most others. I had problems with fat cases near the bottom and this helped, but did not totally solve that problem. I finally just gave up on that and chose to deal with that problem a different way, but am now using the Dillon sizing die which is more forgiving, and it reduced the indexing problem a lot.
It is also possible your machine's part under the shell plate, don't know what it is called, aluminum thing with two Allen screws holding it down, has gotten out of alignment. Dillon has a tool that you can use to re-align everything. They sent me mine for free.
Hope you find some of this helpful.
