You may have signed up to a continued payment authority and if you have, you had to cancel the renewal subscription, when they sent a reminder. I presume they sent an email or some communication that the subs was due for renewal and that they would charge your card with the relevant amount. I think they should have done.

Check with AVG whether you agreed to a continuous payment authority when you originally bought the product. They should be able to confirm this. It will only be AVG and not your card company that can confirm whether a continuous payment authority was authorised by you.

Your card company will only refund the payment and send it back to the relevant company, if it is a fraudulent transaction that you can evidence. As this related to something that you bought, it is up to AVG to resolve.