Hmmmm... Since it is only some of your users it must be something specific to them. Can you ask them if they have any ad blocking/tracking add-ons installed on their browsers? Of if they have cookies turned off/blocked in their browser settings?
If they are, ask them to add your site to their approved websites in the Privacy and Security > Cookies and Site Data settings of their browser.
These two things will mess with logins as there are "good" cookies that are used to facilitate the login process.
Judith "Many of life's failures are people who did not realize how close they were to success when they gave up." ~Thomas Edison