I got banned few weeks ago. My account was 4 months old, had +3k real active users. Average post likes were around 400.
I started getting emails to reset account password because instagram detected suspicious activity.
After 4-5 password resets I got banned.
Wasn't banned because of the speed of likes/comments/follows etc. (as soon as you keep it under the limits you're fine)
I was banned because IG detected that the account was getting using from multiple locations/devices at the same time..
Follow the security tips on Instagress' blog and you'll be fine.
I was using the account as a private one, was sharing pictures I took, so it's really painful because I had a lot of people that really liked my stuff, plus friends and people I met around... and starting again from scratch is a real pain in the ar**e