That's weird...
Cookies are bits of code the web site stores on your computer. In the case of bonsainut, we don't keep any personal information in the cookie other than your credentials (so your browser knows you are logged into the site) and your recent activity (so you know which threads you have read, versus which are unread, which notifications you have seen versus unseen, etc). The error message you are getting is the site is looking for the cookie on your ipad... and can't find it. Usually (as you pointed out) it is because your browser is blocking cookies, or you are surfing the web in "private" or "anonymous" mode.
Sometimes it is due to updates on the site, if the site changes the cookie structure, or places it in a different location. If you are visiting the web site and using a cached version of the site, the cached version may tell your ipad to look for the cookie in the old location, and it generates the error as if the cookie doesn't exist. Refreshing the site usually clears up the problem.
These are hard problems for me to solve, because it almost always has to do with something on your ipad - or the way your browser is configured. I am not aware of anyone else having these problems, so if I can't replicate it here, I can't fix it