All right, fixed the new problem! Fix is here:

http://www.simplemachines.org/community/index.php?topic=155704.15;wap2

Both problems now resolved.

I patched to JSMF 2.0.2.1 (At least, I think I did... I followed the instructions but the About area still shows it to be 2.0.2) and the problem seems to have abated. The session on the forums doesn't end anymore either, I usually stay logged in throughout the day.

Just a warning though, that it may not completely fix things. A new problem popped up, when going from the forum back to the Joomla site I am logged out and have to log back in. It still recognizes my being logged in on the forums though. This is a much less annoying problem and something I can certainly live with over the other one. At some point I hope to figure it out, but for now I feel comfortable allowing people to register and use the site.

First off, my setup:

Joomla 1.0.13
SMF 1.1.3
JSMF 2.0.2
CB 1.1

I can login to the Joomla part of the site fine, and will be logged into the SMF part as well. I can not log into SMF alone, it kicks me back to the Joomla main page without having logged me in. I read that this was a problem in a much earlier version of JSMF and that it would be fixed in the next one. I'm not sure if I'm missing some kind of setting that was added, I've looked numerous times and I don't see anything that seems to apply. I've been searching for a fix for two days, pretty much to no avail. If anyone is able to shed some light on this I'd really appreciate it.

I used this to help me work around being unable to get into my SMF admin account after installing the CB and JSMF bridges. I was getting the message "You are not authorized to view this resource" and the solution offered in the FAQ didn't apply, as my forums are set to public access. Thanks so much for posting this!! I was pulling my hair out.