Ok so lately some of the accounts that I purchased have been getting disabled (sometimes twice in a weeks time) and I managed to get them all back multiple times so I'll share what I did.
If you're receiving a message saying your account has been disabled for violating terms they give you the option of "letting them know" if they made a mistake. As far as my testing has gone, this has worked once for me. If it gets disabled multiple times they will say it CAN NOT be restored. BUT there's a way around that. You can claim that it was hacked!
First go to this URL:
https://help.instagram.com/contact/740949042640030
Click "my account"
Then click NO (even if you can access the email account).
Enter the email address you'd like for them to contact you on.
Enter your username.
Enter the email address you used to set up the account.
I personally chose this option but I think you can use any of them: This account contains pictures that I've created or produced, but I'm not in themI clicked No.
I clicked Someone I don't know.
For how they accessed my account I put "Not sure."
Then upload a photo from your account. I actually don't think this is even that important because on some of my accounts I wasn't even sure which photo was on which account so it may have been wrong.
Then I received an email requesting the following...
1. A brief description of the issue you're experiencing, including the date you last had access to your account and how you lost access
2. The email address you used to sign up for your account
So I sent this exact response (just removed my personal info). The email below is actually true. I was sending them emails from the email address on the account but they kept bouncing back to me for some reason but they did work from a hotmail address I had.
They then responded with this...
I did exactly that and my account was restored within a few business days.
Hope that helps some of you! Let me know if you have any questions.