I voted more than 10, because I rarely give up at fewer than that for my best oolongs, but it's a tossup between more than 10, and more than 15, because my favorite young sheng puerhs demand so many flash infusions for my bitter-phobic palate that I'm often up to a dozen before I actually start letting it steep a bit before pouring.
Today, I started with several more infusions of day 3 of a sample of Lao Ban Pen (2010 or 2011, can't remember) from Norbu, a very nice sheng that was probably up to 20 infusions already.
Then there was an interlude with some very nice Winter Ali Shan oolong, also from Norbu, that was infused probably 7 or 8 times along, but those were high volume/long steeps to prepare a thermos full of tea. As I usually brew for immediate drinking, that would have been 12-15 infusions at least.
Another half dozen infusions of the Lao Ban Pen (home for dinner), and now drinking a white tea from Norbu to get me through a bit more paperwork at the office, and this will probably only go 4-5 infusions.
I stop sooner on white teas because they often go to an unpleasant place between the last tasty infusion and sweetwater, unlike most oolongs, puerhs, and many greens.