Relax, even though the problem seems complicated, the solution is relatively simple.
I just created a long post with screenshots explaining all this, when Firefox crashed, so even among experienced GNU users, computer problems can be annoying. Really annoying.
The long and short of it is this: there are multiple ways to conduct rollouts in GNU. Many of these will lose the rollout data as soon as GNU exits. Only a couple will actually allow you to save it to a file, so that you can open it or extend it later. The GNU team appears to be working on this issue, but it takes a long time. It took me several months of trial and error to figure out a lot of these things. I still haven't learned all there is to know about GNU, but I can tell you how to save rollouts.
Right, then, how to save rollouts (using version 0.16):
1) Start with your regular old starting position.
2) Play the move out. It will now show up in the game log pane. Do not rollout from the hint window.
3) Select the move in the game log pane (i.e., click on it).
4) Go to Analyze (menu) -> Analyze move.
5) The analysis pane should now pop up. You can perform your rollout from there. Alternatively, if you had previously opened the hint window before making your move, you will see the analysis pane pop up.
6) Once your rollout is complete, save your game as an .sgf. Stick described this procedure in his post, I'll put my take on it: go to File->Save, then choose match or game. Do NOT save only the position, this will get rid of the rollout data.
7) Enjoy. Your rollouts can now be saved. If you have any problems with this, just ask; I'm confident that they can be resolved.
Bonus Q's:
Q: Oh God, I knew all this, but I rolled out from the hint window anyway (or from Analyze menu -> Rollout). Is my rollout lost now?
A: It used to be this way. However, in the latest version of GNU, if you simply make your move (or double for a cube decision), the analysis pane should pop up WITH all rollout data intact. Neat, huh?
Q: In some way related to saving my rollout data, I often post cube problems with the dice rolls shown on the board. What is a simple way to get rid of those?
A: I couldn't recreate what leads to this exact problem. There are a couple of different things you could try: after clicking double and take, you can then close the manual dice window, either by pressing Esc or the close button. Alternatively, you can just clear the moves and/or analysis following the cube decision, so long as you don't save.