Using AutoCompleExtender from the Ajax Control Toolkit, if MinimumPrefixLength=0 and CompletionInterval=100, and you click slowly on the textbox (as in leave >100ms between pressing and releasing the mouse button), the dropdown appears and then immediately disappears.
The sample website has MinimumPrefixLength=0 and CompletionInterval=1000 so to see the same effect you don't see the same effect.
(Raised as http://ajaxcontroltoolkit.codeplex.com/workitem/26996)
(Reproduced in IE7 and FF4)
(Updated 24/08/11 with information about being related to CompletionInterval)
My current workaround is to set CompletionInterval=400. Although this makes it less responsive, it seems a fair compromise between the time it take to press a mouse button and the time the user expects to wait for suggestions.