In the WM_MINMAXFRAME message hide the offending control.
case WM_MINMAXFRAME:
{
PSWP pswp; /* pos change structure */
/* hide list box when minimized so it doesn't overwrite icon */
pswp = PVOIDFROMMP( mp1 );
WinShowWindow(
WinWindowFromID( hwnd, IDD_FILES ),
!(pswp->fs & SWP_MINIMIZE)
);
}
break;