For those experiencing this -- Please check if you have the browser extension uBlock Origin enabled. If so, temporarily disable it. If that stops the MFA from looping, then that means you will need to unblock the associated QB Online blocked script inside of uBlock Origin.

If you do not wish to disable uBlock Origin, you can extend the duration of time before QB Online times you out to be 3 hours by going to the Gear Icon → Account & Settings → Advanced → Scroll down to Other preferences → Adjust Sign me out if inactive for to be 3 hours instead of the defaulted 1 hour. This won't resolve the issue, but it will decrease the number of instances you are asked to do MFA.

Asking your ISP to switch you to a static IP may help as well.