There are two reasons an app may be blocked for your app users.
The App is Paused
You (the app creator) may have paused the app. This happens on the Manage > Deploy pane of the app editor. If you hit the Pause button, this prevents users of the app from making any changes to data and syncing the data successfully. When they try to sync, they will see a message: 'The app creator has blocked all data updates'. To fix this, go to the Manage > Deploy pane of the app editor and hit the Resume button.
The App is Blocked
This happens when you have an account alert (an issue related to billing) that stays unresolved for an extended period of time. Any such issues are brought to your attention in three ways:
You will see an alert symbol in the top bar of the web site and also more details on the Account page
After a couple of days, all users of your app will see a warning message on the sync screen
You will receive three email messages over a period of a week informing you of the problem
If the account alerts are not resolved after a period of time (approximately 9 days), the system finally blocks your app. At this point, your users will see the message: 'Error: app blocked'. To fix the problem, please go to your Account page, check the account alert and address it. Once the alert is no longer shown, each of your app users will need to run Sync once. This will fetch the latest app definition and their apps will then start running as expected.
Usually, customers end up in this state because they did not see the email alert messages. Please check your email settings and ensure that email from AppSheet is not sent to your junk email folder.