If you are having problems with not being able to stay logged in here are some of the common reasons and possible fixes.
PHP VersionAs stated on the download page you need to have PHP 4.1.0 or greater installed. If you don't you won't be able to login. If you don't know what version you have create a
phpinfo() page.
No $cookienameCheck your Settings.php file for a variable by the name of $cookiename. If you don't see that then you need to add it. This problem usually arises when upgrading to 1.5.1 from past versions and not running the upgrade script.
Bad charactersYou can only use alphanumeric characters for the name of your cookie. Other characters are likely to cause problems.
High Security LevelsIf you or your users are running IE you will need to have your security lowered to the medium setting or add your domain to the allowed sites list.
Time ProblemsIf your server time is wrong
or the users time is off then the cookie may not save properly. Be sure both are correct.
Wrong DomainSometimes the cookie saves under the wrong domain. If this is the case try selecting store cookies locally in the admin mod settings page.
Different YaBBSE VersionsYour YaBB files should all be the same version. Do a detailed version check or re-upload the Sources directory to be sure.
These are all the common problems that come to mind, post below if I've missed any.