The phrase "eleventh time" means something that happens repeatedly or is done many times. It refers to the action or event occurring on the 11th occurrence. Full definition
Next time you're there and have gone over the new releases shelves for the eleventh time and only to be enticed by some movie featuring Ice - T or Lance Henriksen because there's just nothing else there, I would suggest you forget such foolish notions and give this one a shot. (qwipster.net)
You surf through the news, see what's happening on Twitter and check your e-mail for the eleventh time in ten minutes, but still — nothing. (selfpublishingteam.com)
I've just completed The Stanley Parable for the eleventh time. (pcgamer.com)