After the purchase is confirmed by Apple, the app sends this information to Avast, which will process the purchase and then generate a subscription code for that and return it to the app.
It probably happened that the communication failed at that point, so you didn't get the subscription code.
Can you tell which version of SecureLine you were using when you bought the subscription?
If you were using version 3.1, you should have the auto-renewable subscription (please confirm), which should be possible to be restored by tapping that button on the top of the subscription screen on the SecureLine app.
But you need to be sure you're logged in on iTunes with the same account you used to purchase the subscription. (Device Settings > iTunes Store & App Store > Apple ID).
If that happened when you had version 3.0, then you had the non-renewable subscription, which is not possible to restore via iTunes, so you will need to provide support the receipt you got after the purchase.
I'm sorry for the inconvenience, but please double check this and make sure, it can save you some time.
Kind regards,
Jobert