The way Shopify has built their subscription billing for apps is different than a regular credit card subscription works.
Shopify's subscriptions have a limit on their usage charges which means that after the limit is reached the account cannot be charged for additional usage. There is also no option to upgrade a plan automatically once a certain limit has been reached for a smoother process.
That's why we - permanently - display messages at 3 different stages in the dashboard:
80% of monthly included volume
first warning - permanently displayed
100% of monthly included volume
second warning - permanently displayed
more than 100% / Usage charges
the exact number of remaining returns is permanently displayed based on the remaining usage charge amount
e.g. "Your customers can start 498 additional returns. After that customers will not be able to start a return until the end of the current billing period due to Shopify's usage-charge limit on your account. Upgrade your plan now"
This warning gives accounts usually at least 2 weeks or more of runway to have a user with billing privileges upgrade their plan. As mentioned the exact number of remaining returns is displayed right in the dashboard.
Recommendations
Choose a plan that easily accomodates your monthly returns volume for a smooth process on your customer's side
In times of increased return volumes (e.g. Christmas, BFCM) upgrade your plan temporarily to a higher tier. You can downgrade at any point later
Set up a process with your Customer-Support staff to inform a store-admin at one of the described 3 stages about a plan upgrade