I think your rip fence is located too close to the blade, after the cut. There is no extra space for the strip to go to, and bing thin and springy, it just bounces back.

You could put in a spliiter or kerf keeper, but this must be EXACTLY the same width as the kerf, or just a few thousandths thinner. If you made it thicker than the kerf, then it will do one of two things. It will either trap the thin strip against the fence and bind, or it will force the end of the board away from the fence, and give you strips with variations in thickness.

There is a reasonably simple way to change this though, and that is to provide some area after the blade for the strip to move into. To accomplish this, you want your infeed fence to stop at roughly the middle of the sawblade -- and you do this by adding a strip of scrap wood to the face of the fence. Let's say you get a 2 foot long piece of 1x4, set it on edge, and clamp that to your fence so that one end is by the blade, and the other extends off the infeed side of the table. Of course you will need to move the fence about 3/4 of an inch away from the blade to accomodate this addition. Now you will find that after the cut, your strip has a roughly 3/4 inch area in which to maneuver, and stay away from the blade, while it is still on the table. Of course after it clears the table and the end of your fence it can move as freely as you allow.

This works fine for the first few feet of your cut, as the board can slide along that 2 foot fence extension and be supported by it as it hits the blade. As you get to the end of the board, however, the area of the board in contact with the fence decreases rapidly, and you end up the cut with almost no control.
This is a bad thing, so we add another control to the saw table, after the blade. This control surface must be aligned so that it is in line with the outside edge of the sawblade, and it can't be any wider 3/4 inch, or however thick your fence extension is. If you need a wider piece, make the fence extension from thicker stock. A small "C" clamp with a scrap of wood, or even by itself can work well. This MUST be mounted securely. Think of this as a well mounted splitter, or an "island" fence.

Here is how it works: As you start your cut the board is forced against the extension you built on the infeed fence. As teh cut progresses, the new strip is guided between your "island" splitter and the actual rip fence -- remember you now have that 3/4 inch space to play with. As the strip goes off at a slight angle the board now rests on the side of that "island", and also on the infeed fence. For the remainder of the cut the board has two solid support points, the extended infeed fence and the island, so it can feed straight right up to the very last inch.

Hopefully this will give you long, straight cuts.

hope this helps

PGJ