Mac OS X: Saved Application State causes non-modal QDialogs not to appear

My application uses a number of non-modal QDialogs. On updating to the Cocoa-based Mac OS version of Qt, the application fails to show non-modal QDialogs on the screen. This happens from the second or third invocation of the program. Qt thinks the QDialogs are visible (isVisible). Raising the window again, hiding and reshowing, or changing the position does nothing. If the user clicks on the application icon in the Mac dock bar, the QDialogs appear again. Alternatively, bringing up a modal QDialog causes the windows to appear.

I have tracked it down to the information stored for the application in ~/Library/Saved Application State/com.mycomp.myapp. If I delete this directory, this fixes the problem.

I've been unable to replicate the problem using simple test cases. I'm not sure how to proceed to fix this (other than deleting the offending files on every run). I assume it is something to do with Mac OS trying to restore the window states.

I've attached an XML-converted version of the windows.plist file from the Saved Application State when the app is showing the problem.