The save button is grayed out, so there is never a file made at all. I'm not sure it's a permissions issue, because I can save the libraries (indeed, I've been making do with doing my editing there!), but I get the idea it's supposed to be able to save actual projects...
Yes, the demo should be able to save project files. (Note that this is not the same as "saving output" or rendering. To do that, click the red "save output" button.)
When you click the "save" button and the dialog opens, make sure that you've chosen a folder where you have write access (like "Documents" or "Desktop"), and type a short, simple filename for the project. See if that helps.
Also, make sure you're not using an old version of the demo. If you recently (in the last month) downloaded it directly from our site, you should have the latest.
As far as I know, I have write permission--every other program saves fine, I can copy/paste things without trouble. ParticleIllusion itself makes video files of the particles just fine, and it can save the library file, but not the project file. I downloaded the demo last week.
Ah well. Thanks, though..