I've read that the interruption is to allow whatever eggs haven't hatched or been killed to hatch and be killed! Apparently, some eggs don't respond to these remedies and are not killed. The only recourse is to kill the adults, give the eggs an opportunity to hatch, and then atack them with the next round.
Not exactly sure where I read it and I'd prefer to provide the complete source, of course, but I thought a response was warranted regardless. Hope it helps.