A good question! I'd say the interruption can only happen once. So once the Interrupt Clock is filled, the players weave it into the story and resolve it, and then it can't happen again. 1-3s are now just whoopsies, with no further clock segment ticking.
I am open to changing the dice array though, since I did not playtest this game, but based it off another. If you do play, I'd be keen to hear your thoughts :)