The recent Joomla! 1.0.13 release/update has caused a few problems with a whole host of extensions, and unfortunatley JCE was not left unscathed. Fortunately, the effect seems to be localized, and as it turns out, not too difficult to fix (once I found the where and why!).
Problem: If you click on a file/image name in any of the Manager plugins, you are redirected to the Admin login screen.
Reason: Not too sure why, but the 2 simultaneous ajax requests to index2.php causes the logout.
Solution: Force queuing of requests so only 1 is processed at a time.
Download the zip file below, unzip contents (utils.js and utils_src.js) over original files in mambots/editors/jce/jscripts/tiny_mce/libraries/jscripts. Clear your browser cache. Open the plugin window and refresh using CTRL+F5 (this is very important as it clears out the old javascript files and forces a reload of all files).