http://bugs.winehq.org/show_bug.cgi?id=10643
--- Comment #8 from markk@clara.co.uk 2010-04-15 11:55:40 --- WinUAE version 1.5.1 beta 6 and later support a "-rawkeyboard" command-line argument. If you specify that when running WinUAE, it uses a different method (not DirectInput) to read the keyboard.
For me, running WinUAE that way ("wine winuae.exe -rawinput") does not have the "stuck key" problem, and the settings window goes away as it should. Without -rawkeyboard the problem remains.
If someone wants to figure out what the problem with Wine is, maybe examining the source of a recent WinUAE version could help, to see how its keyboard reading differs when -rawkeyboard is used?