I don't know if this is your issue or not, but I had an issue on my Intel MacBook where, after opening/closing certain applications or after an arbitrary amount of time, my minimize button would become grayed out. It seemed to affect Carbon apps more than Cocoa, but...
Killing the Dock.app process manages to restore the ability to minimize until it fails again. Mine was fixed by deleting ~/Library/Preferences/com.apple.systemuiserver.plist and ~/Library/Preferences/com.apple.dock.plist. EDIT: I think the problem child lies in the first file, rather than the latter, but since killing Dock.app temporarily restored the ability to minimize, I opted to trash it as well. Log out and log back in, or restart, this will then reset your Dock and Menu Extras to their default state. I did this months ago and haven't had the issue since.
If you wish, you can make backups of these two files by copying them elsewhere and restore them if it doesn't fix the problem.