Pop-up windows that disappear mysteriously

Is it when you launch an application?

I have a similar behavior with jDownloader, and it seems to be the Firewall (Allowing the app to make a connection) popup.

I don't have a solution, it's still happening, but since I don't have any trouble using the app, I haven't looked further.

Since the app is based on Java, maybe OS X Lion notice (after showing the popup) that Java is allowed to connect and cancel the prompt. It's purely based on assumption and I wouldn't be surprise to be proven wrong but I can't find any other reason (since it's only with this, Java-based, app that it's happening)

Go to System Preferences>Security & Privacy>Firewall>Firewall Options and add an incoming service: Library/Java/Home/bin/java

Save settings/close the lock...you are done.