I looked around some. Yuku has changed things from Ezboard. Now, if I log out and attempt to reply or add a message, the first thing Yuku does is prompt me to log in, and it throws me into the reply or add message screen. And then I stay logged in, it's not just to post one message.
As far as your getting logged out... Ezboard uses cookies to track your login and to stay logged in. I'm guessing that either your browser's cookies are getting cleared. Or, Yuku may be sensitive to IP address. Your internet connection may be rec-connecting at a new IP address periodically, like after quiet periods, and Yuku regards it as a forced logout.
I use Firefox to view Yuku. I enabled Firefox to save my user name and password, to make it easier to log in again (basically the username and password boxes are filled in for you). I recommend at least doing that.
