In Flash, why does "Block all sites from using the camera and microphone" keep getting unblocked?

First things first, disabling Camera/Mic access in Flash Player is probably not going to protect you from modern variants of that kind of attack.  If you want to spy on someone, you don't want the camera's recording light to come on, so a good attack is going to target layers way underneath us.

This article provides solid, practical advice, but the bottom line is that you want physical solutions that can't be circumvented in software: How to Keep the NSA From Spying Through Your Webcam | WIRED

That said, the settings you're talking about are stored in a configuration file called settings.sol.  When I see this behavior, it's typically either that the filesystem is corrupted and we're unable to read/write reliably to that location, or we're otherwise restricted by something underneath us (mangled filesystem permissions, OS changes, etc.) from reliably accessing that file.  I also know of at least one security snake-oil plug in for Firefox that blows away the Flash "master cookie" purportedly to protect privacy, but all it's doing in practice is resetting Flash Player back to it's default settings.

https://www.wired.com/2014/03/webcams-mics/

The settings file itself should be here:

/Users/you/Library/Preferences/Macromedia/Flash Player/macromedia.com/support/flashplayer/sys/settings.sol

A couple things you could do to figure out where the problem is:

• Flash Player and Safari share a Flash Player installation, so if your custom settings aren't working in Safari, but they show up in Firefox, Safari is restricting our ability to read to that important location.  I don't think that this is the case, but it's not outside the real of possibility and it's easy to check.
  
  
• If the changes aren't showing up in either place, it's probably time to sanity-check your filesystem.  Filesystem corruption can be an early indicator of impending disk failure, and the processes of checking it out will give the disk a decent workout.  I'd strongly recommend backing up any important data before exercising the drive, just in case.  Data recovery services are expensive.
  
  Once you're confident that anything irreplaceable is safely backed up, you'll want to use the Apple Disk First Aid utility:
  
  See the "Try Disk Utility" section:
  https://support.apple.com/en-us/HT203176
  
  While you're there, choose Repair Filesystem Permissions (Verify will frequently return clean, but then Repair will still fix a bunch of problems).
  
  If it detected and repaired errors, you might just want to do an uninstall/reinstall of Flash Player to ensure that everything is in a reliable state, then make your changes again.  This is *usually* what's going on with most people that have this problem, and  your changes will probably start sticking again.
  
  Uninstall Flash Player - Mac:
  https://helpx.adobe.com/flash-player/kb/uninstall-flash-player-mac-os.html
  
  Install Flash Player:
  https://get.adobe.com/flashplayer/
  
  
• If that doesn't help, or disk first aid doesn't reveal problems with the filesystem or permissions, then we need to talk about that third possibility.  What are you using/doing that might be interfering with normal Flash Player operation, such that we're unable to depend on the contents of our config file?