ChrisChinchilla how often does this dialogue come? For the sake of testing, the monthly and yearly subscription run quicker than the actual month and year. So if you started a monthly subscription for the TestFlight adoc studio version, chances are that you'll need to repeat subscription actions really soon.
According to the following list, 1 month is 5 minutes in the TestFlight sandbox, 1 year will be 1 hour:
Remember: the TestFlight adoc studio version won't bill your AppStore account.
Here the screenshots for the expected procedure... Personally I click on yearly subscription, so I don't need to repeat the actions too often.
Or do you mean, you select a subscription, enter your appleID credentials and confirming the subscription etc never completes?