Staying logged in is related to cookies.
If you log in and vb3 is able to properly set a cookie in your browser to remember you're logged in, then everything is great.
If vb3 cannot properly set the cookie, then you're logged out as far as its concerned. WWW sites can set cookies so they expire when you close your browser or at a specified date and time in the future. When you click the "remember me" checkbox when you log in, vb3 sets the cookie to expire some really long time in the future. If you don't click the checkbox, it sets the cookie to expire when you close your browser.
Every time I have worked with a site user who's complained about this kind of thing, it is some software they've installed on their computer. Like zone alarm firewall software. If you are blocking cookies (a setting in your browser), obviously the login isn't going to work right.
My recommendation at a first thing to try is to clear your cookies. The various browsers have different pulldown menus to do this. In chrome, CTRL+SHIFT+DEL brings up the "clear history" dialog. You only need to erase your cookies (you need to look at what's checked on that form!). In IE8, tools menu -> internet options, Browsing history tab (first one), delete... button brings up a similar form. In Firefox, CTRL+SHIFT+DEL also works, or tools -> clear private settings.