The site knows whether you're "logged in" by setting a cookie, so first check that your browser is enabled for them. I think it must be, because otherwise you wouldn't be able to vote even once or twice.

Sometimes following a hyperlink that hasn't been set up right can make you appear to be "logged out". The reason is that both "perlmonks.org" and "perlmonks.com" lead here, but only one of the names is in the cookie that is set when you login. If people use the built-in syntax (i.e., the [square brackets]) to create links within the site that won't be a problem. However, sometimes people use a standard anchor tag (<a href="...">)or a square bracket that defeats the normal mechanisms (like [http://perlmonks.org/...]), and those can cause the problem. For example, if you normally use "perlmonks.org", this link will appear to log you out, and if you use "perlmonks.com", this one will do the same.

As for refreshing, it's better to use the talk button than hitting refresh in your browser. I'm not sure why you don't want to use it, though. Maybe if you describe why that's a problem, someone can point out an alternative.