Reply To: BuddyPress and WPLMS Plugin, login issue, cookie is ignored?
Try disabling ajax login in WP Admin – WPLMS – BuddyPress
In all PHP & Cookie based login systems you will most likely need to refresh the page from the server. It may happen that when you refresh once, the browser shows as cached version, to confirm just change the url by adding a url/?1 ?1 parameter in your url to force browser to consider it as a new request.
IF you are using version 4, this issue would not appear. The login system is built on JWT, so it happens instant without page loads and there is no nonce passed here, so you can cache your pages for eternity as static html and get better page loading time.