Using Dr. Java 20130901-r5756 on a MacBookPro/OS 10.6.8.
If you have changed your source file and either Quit (cmd-Q) or close the file with the close-file (red) bullet, the cancel/no/yes Save changes dialog comes up, but if you select "cancel", Dr. Java terminates as if you had selected "no". Interestingly enough, this behavior does not happen if you close the file via cmd-w or with Dr. Java's "close" button. The "cancel" button works as expected in that case.
This is fixed in drjava-beta-20160913-225446.