How to have an async endless loop with Promises

How can I achieve this?

Not with a blocking loop since promises won't be able to settle. You can learn more about JavaScript's event loop on MDN.

Instead, call the function again when the promise is resolved:

Promise.resolve().then(function resolver() {
    return someAsyncFunction()
    .then(doSomething)
    .then(resolver);
}).catch((error) => {
    console.log("Error: " + error);
});