Because the login screen is directly from Instagram, it is completely controlled by them and is why you are not being redirected to Plann again after you enter the security code.

We've spotted an issue recently for some who have 2 factor authentication turned on in Instagram. We are working on getting this sorted for you. Plann’ers who have turned off 2 factor authentication inside of Instagram have come back to Plann and found it working.

You should then be able to log back into Instagram and switch two factor authentication back on again.

Again, we are still investigating and will definitely let you know when we have an update!