According to "The Changeling," Nomad's weapon packed the punch of 90 photon torpedoes and reduced Enterprise shield power by 20%. The shields could withstand 3 more attacks and the 4th would "shatter" them.
So the Enterprise could take 360 torpedo hits before the shields were weakened to the point of failing. Somewhere between 360 and 400 torpedos would take them down.
I don't think the shields were ever this powerful in other episodes.