Stripe itself does not control subscription duration, it doesn’t have that functionality, so it’s controlled by our plugin. It relies on webhooks to do this. If there is a problem with those, it cannot control subscription duration so it lasts forever.
The situation you described doesn’t seem normal. If you’re sure both of your API Key pairs are valid (Live and Test Secret and Public keys), can you provide the access to your WP Dashboard so I could have a look from inside? Please send those via this form https://s-plugins.com/contact-us/