Same issue here. Though I suspect it may be a" multiple" account issue.
I've always had 3 or 4 Amex cards, and have had no problem updating them all at once in the past. Recently, however, I opened an "Amex High-Yield Savings Account," and noticed that it added a new "Financial Institution" to my One Step Update list. Specifically, there is the old FI named "American Express" which says "4 accounts updated" (i.e., my 4 credit cards), and now there's a new one named "American Expresss - Banking" that only says "1 account updated," which is the new savings account. I suspect this new account is the one constantly prompting me for 2-step verification since the issue only just recently arose with the addition of this new account.
Anyway, I will disable the Update for the new Amex account and see if that helps. I also note that if I just "Cancel" the 2-step request, Quicken appears to update anyway. It might be just not updating this one account. I'll come back with more info after trying some solutions. Thx.