Nothing. The security never said anything about stopping saving.
If you think Acrobat should be able to stop this, then think about what would happen on a system without Reader; the user is just prompted by the browser to save the file.
Nothing in the world can stop ANY file from being saved, shared, emailed etc.
But DRM exists so that you can control who OPENS a file. This is an enormously more complex and costly thing than setting security.
See this for background
Adobe's offering is LiveCycle Rights Management (which naturally requires a server of your own running 24/7 in order to check permissions). There are third party options.
Thank you for your reply. It's become clear to me that I'll have to look for other ways to make my lessons!
If a file can be be viewed in a browser, then the file is being be downloaded. You cannot stop this, you can only make it more difficult for the client to use the downloaded file. This has nothing to do with pdf files, but how the internet works. You can stream a movie. You can make it difficult for someone to capture it. But with the right tools, it can be done. You are trying to solve an insoluable problem.
With DRM, you can limit the number of times a file can be opened. You can limit the the number of days a file can be viewed. You can limit the computer it can be opened on. If a client can only view it once or twice for for one week or two, why do you care if they have the file on their computer? With DRM you can prevent printing if you wish, with some DRMs, you can even prevent screen shots, but if the client can view the file, nothing can stop them from taking a picture of the screen with their camera.