Ok, I have spent over 3 hours on this issue. (You will get my bill in the mail... just kidding.

) You even had me thinking maybe it was a bug I had overlooked, even though the problem only happened on your website.
I thought maybe you had put a script in your content (nope), or some of the other usual suspects.
However, I finally did prevail... I must say this one was something I had not seen before.

one for the "history books".
Here is the offending content I finally found in your home page after much searching:
Code:
<img alt="" src="http://valleyshore.toastmastersclubs.org/index.cgi?adminauth+3940+jX5hnrSw6S8RHHRd1TgXxCj5z" />
This was located right before the code for your gif images, so I looked right past it several times. The problem with this is that somebody put this page address that causes logouts on the server in for the image address. So every time you would load the home page it would always log you out. Unfortunately, since logouts are not always immediately shown unless you trigger them, you never knew you were already logged out on the server when you loaded the admin console. The admin console only looks for the tracking cookie on your computer for logouts... it does not contact the server until you do a save.
I have to say this is insidious as far as user oops go... no script was involved, just an ordinary image img tag that everyone uses.

I had to wipe your home page content then restore it later w/o the offending code just to do the fix.
BTW, your website is working again.