I can create a user account but it doesn't save my password for me to log back in a second time. I've tried added the password to the account in phpmyadmin but that doesn't work either. Does anyone have a solution to this issue?
Which Magento version you are using? Have you installed any login related extension recently like social login?
Are you installing magento in localhost? If yes, I think you meet the problem with cookie domain. Try to install it on a domain in hosting to see if it still happen.