Aggressive Mac OS X Dock bouncing during modal dialog

I've observed this bug in the Anki app during syncing:
https://anki.tenderapp.com/discussions/ankidesktop/1043-crazy-jumping-in-mac-os-x-dock-during-sync

When the app is in the background and processes events while a modal dialog is open, the app's Dock icon jumps too quickly.

What I found out during my brief debugging session: -[NSApplication requestUserAttention:] (which causes the Dock jumping) is called by -[NSApplication beginModalSessionForWindow:], and beginModalSessionForWindow is called more often than necessary because temporarilyStopAllModalSessions() is called when processing events, which causes the next call to currentModalSession to call beginModalSessionForWindow again.