Too Many Redirects on Logout and Login Cache Problem

I am running a WP membership site with around 150 members, so not huge numbers. I have got a couple of problems on it that I think may be related.

Firstly, occasionally when a user logs in WordPress is convinced they are already logged in, and takes them to a page asking them if they need to log out. They log out, only to be presented with the same question on the next login. If they clear their Cache the problem is solved and they can log in without a problem.

Secondly, on logout I am getting a ‘Too Many Redirects’ error briefly displayed prior to my ‘goodbye’ page. My site address is set up correctly etc.. and this is the only thing I can find that could potentially be causing that problem.

I’m not sure if these problems are related, but I have a sneaky suspicion that they are, any help would be appreciated.