Given the ability does not state "the fist time you make a successful run" but "whenever you make a successful run...", you can...
**** SPOILER ALERT : UNPLAYABLE STUPID COMBO ****
...run unprotected archives 4 times a turn (yes, all your clicks), 10 turns in a row. 4 times a turn makes sure runner won't get a new card (mandatory draw + 3 clicks). Do this 10 turns in a row with Datasucker, Desperado and John Masanori in play.
After this break, game resumes.
But meanwhile you have shaped the perfect hand, you have 40 credits and 40 virus tokens on Datasucker. You're ready to win.
If Corp purges virus counters, head for another 10 turns :) Stalemate. Force the draw in a tournament if you're in a bad situation.