I have now discovered through some trial and error that if I override JuceNSWindowClass::isAccessibilityElement and return NO that I can prevent the instant popup dismissal. Obviously this is not ideal, since it means that the main JUCE window is no longer participating in accessibility. Then again, it’s not much of a loss, since due to JUCE’s architecture, it’s not navigable via accessibility anyway. [See this discussion: Juce Accessibility].
I’m curious if a change like this would affect anyone and if there’s some better approach that could be taken to handle the problem.