As a side note to this, if you have your taskbar on a secondary monitor, the reboot prompt window thing appears over there instead of on your primary monitor, so it doesn't get hidden by full-screen apps. (At least in Vista. I haven't seen the popup in 7 yet.)
I'm gonna guess that the issue here is exclusive control of the video device, blocking the reboot notification.
Starting with Windows 7, MS is trying to fix that problem. Should be part of new certification requirements I guess? I'm not quite clear on that part, but the basic info about it in relation to compatibility manifests is here:
http://msdn.microsoft.com/en-us/library/dd371711(VS.85).aspx
DirectDraw Lock
- Windows 7: Applications manifested for Windows 7 cannot call Lock API in DDRAW to lock the primary Desktop video buffer. Doing so will result in error, and NULL pointer for the primary will be returned. This behavior is enforced even if Desktop Window Manager Composition is not turned on. Windows 7 compatible applications must not lock the primary video buffer to render.
- Windows Vista (default): Applications will be able to acquire a lock on the primary video buffer as legacy applications depend on this behavior. Running the application turns off Desktop Window Manager.
That's assuming this Flash app actually took exclusive control. If its full-screen mode is just the same kind of thing as hitting F11 in a web browser, then I dunno why the OP wouldn't have seen the shutdown pop-up. (Unless the reboot pop-up isn't set to be always on top? Surely not...?)
EDIT: Well I'll be damned, it's not always-on-top. So, if you were working full screen (with the taskbar not visible) and it popped up and right that second you clicked on the window you were working on, you could probably hide it so fast you don't notice.
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On the topic of program behavior itself:
Some apps, such as MS Office programs, when they receive a shutdown signal, will save your work and reopen automatically once rebooted. But they still give you a "save or don't save?" message like the OP experienced, which can be confusing due to the time limit, as the OP also experienced. It's a compromise to deal with both shutdown-aware and non-shutdown-aware apps in situations where the user is present when not present, and to not delay shutdown too long.
The question is, should apps even prompt you to save when it gets a shutdown signal, or would it be better to just auto-save and restart with no prompt at all, to avoid mistaken button presses? That's the sort of thing that really needs an option setting on the app so the user can set as desired. (If this Flash dev program isn't even shutdown-aware at all, then it just sucks.)