this is not a full answer but probably of use to gain more information about your problem. I guess it’s related to cookies but that is really a guess only.
To find out more I suggest a combination of two tools: One Firefox and a wordpress Add-On.
No Redirect Toolpress Strict Edition (Firefox Add-On)
On Toolpress in the tools folder, you can find a Firefox Add-On that is tracking every redirect and can prevent automatic redirection on those. It’s called NoRedirect 1.2.4 Toolpress Strict Edition (Firefox Add-On).
Install it, restart Firefox. Then go to Menu: Tools -> NoRedirect which opens the configuration dialog. Enter a URL pattern like ^http://.* and uncheck the Allow checkbox:
You will now get a notification prior to any redirect:
You can click the link in the grey area. The website you see is the redirect body which is generated (here by stackexchange).
WordPress by default does not return and HTTP Body for redirects which is getting the HTTP specs wrong as HTTP clients do not need to redirect automatically.
Better HTTP Redirects (WordPress Plugin)
Next to that grab my Better HTTP Redirects Plugin. It deals with the wordpress core defect and returns a HTTP body for each redirect. There is a hook available called redirect_hypertext in which you can hook into (or just hack this plugin which is must-use compatible as well) and output the backtrace that caused the redirect (hint: xdebug).
Power of the two:
The firefox plugin will ensure that you’re not getting redirected without confirmation and the wordpress plugin will taking care to display debug information. This hooktracer tool (SJ Hook Profiler) might be of use as well but I have not used it so far.