As promised, I have fixed this disappearing icon issue and released a new beta. You can update from within the non-Mac App Store version in the Updates tab by ticking 'Show Beta Versions' - after ticking that it should prompt you to update to the latest build.
Otherwise you can get the latest version from http://aptonic.com/dropzone/latest
The latest version is Dropzone 2.8 Build 731. This info is given at the bottom of the Updates tab so you can check you are running the right build.
Please let me know how you get on with this version. It has been thoroughly tested and I'm confident it should work without any issues now. I sent you a license for the non-Mac version also.