Make sure the toolbar is not hidden. You can unhide it from the View>Toolbar menu by checking "Travel Time Platform toolbar".
You probably have more than 10 points. The API is limited to 10 searches per query, so that when you have more than 10 points, multiple calls will be made to the endpoint. You will need to run QGIS's union/intersection algorithm as an additional step.
Each API key has a quota of queries. As the plugin can run queries in batch, it is very easy to reach that quota, after which it is not possible to use the API anymore during a cool down period.
To avoid running into this problem without you noticing, the plugin sets an alert level at which the execution get halted. Unless you actively disable the limit or reset the queries count, the execution gets canceled.
If this behaviour is problematic, you can disable the API warning altogether in the plugin settings.
The plugin is quite new, meaning that is very likely that you will run into bugs or issues. If this happens, please look if the issue is already listed on the bug tracker (there may be a solution already), and if not, please report a new issue.