By default, Intuitive Shipping will set your Scenario Visibility to "Off". If you tested your rates with success before turning Testing Mode off but they're not appearing in your live checkouts, this could be the issue.
Head on over to [Menu] > Shipping Scenarios. From here you will be able to easily see which Shipping Scenarios are turned on, and which are turned off. To tun on a Shipping Scenario simply edit the Shipping Scenario, set Visibility to "On under the General Settings and [Save] the changes. Give a test order another go to see if the rates start returning as expected.
I've tried that, but my rates still aren't appearing during live checkouts...
If Visibility is set to "On", another cause could be Carrier Calculated Shipping Rates not being enabled in your store. Shops that do not have Carrier Calculated Rates enabled should see a red banner within the Dashboard of the app. If you have Carrier Calculated Rates enabled and you're still experiencing issues, please submit a support ticket and we'll be happy to investigate the issue further.