I keep getting 401 error recently although it worked correctly for the past three days. I even created a new API key ,but the result is same
API key : a34f497b1cfd7087791f610a0bb8e32d
In the case of exceeding of free API limit, you will get error 429, not 401.
Please check FAQ for possible reasons https://openweathermap.org/faq#error401.