I can't remember the exact instagram options but you need to click through their help centre to where you get them to send you a copy of their privacy policy by email - they take your email address off the list that instagram doesn't send to at that point.. and verification emails will start to...
I know that if an Instagram account needs to send verification emails to an old yahoo email address then there are problems even if the yahoo email account is reactivated.
There's a convoluted way of getting around this not worth explaining if that isn't the specific issue here.