The problem may occur since the entered data hasn’t been processed properly. M2E Pro uses AJAX POST requests to process and save the updated information on the web page, for example for processing info forms. But if your web server executes HTTP redirect by GET method, all POST requests will be redirected to the same URL and the updated information will be lost.
As a solution, you can disable the redirects for all POST request in the configuration of your web server, most probably in the .htaccess file.
Usually, the redirects are disabled in the server configuration for all admin URLs, so you have to disable them for M2E Pro URLs (which contain /M2ePro/) too.