I have the same problem when signing in to QB online.  It will sometimes go for a couple of weeks of not requiring verification and then I will have to verify two or three times in the same day.  It gets very frustrating.  A coworker has the same computer system I do and has never had to verify.  In response to your explanation above, the two-step verification is disabled, I always use the same computer (imac), the same browser (chrome), and I have never cleared my cache.

Thanks.