Stripe: How To Avoid Calling The API Too Often?

Check out the Stripe Webhook API here: https://stripe.com/docs/webhooks

You can store the user's information in the database and only update those fields if the user makes a UI action and you can make an assumption on what to update (like a subscription plan ID) or using a webhook handler, which you can use as a sanity check as well.

To be even more specific, I can give some examples as you will still need to make API calls when a user does an action such as: creates an account, removes their subscription, subscribes to a different subscription. You will store when their subscription expires in the database. When the user makes a request you do not make an API call to check when their subscription expires, but check the database field. When the subscription renews itself you will then have a webhook handler to update the expiration date in the database.

Essentially how it works is Stripe will make a request to YOUR service only when it needs to, instead of your service calling to Stripe on every request.

For WordPress specifically you can user the User Meta Data to cache/store the user's information and only make calls to your database for faster transactions. http://codex.wordpress.org/Function_Reference/get_user_meta