Hi, Does the normal product checkout work (just to identify if the checkout issue on your site is happening with the subscription or not)?
Please enable the debug logging option then do a test so you can see if the log file has any error that it is reporting:
Are you doing live or test mode transactions? Is the subscription plan created for the correct mode (that you are testing with)? If you created a subscription plan in test mode, you can’t use that for live mode. Need to create new subscription plan for live mode (since the plans are not interchangeable).