The error message, when the login details are wrong, doesn’t show up. It may work on the Forget Password page and on other pages, but not on the Login page. How can you fix this?
In all the cases where we've seen this happen, it has come down to the server environment. The primary cause of this happening is if the login page is being cached. The first thing to do would be to ensure that you have caching turned off for this page at both the server level (i.e. varnish caching) and at the site level (i.e. a caching plugin). Once you've done that, if the issue still persists, then as another option, you could opt to use the WordPress login page instead: Configure the Default Login Page