If explorer closes right away, it may be encountering some file which is corrupted or some storage area it can't deal with.
Since Explorer is not normally involved in ejecting a USB drive, it may be related to that. Could you describe the USB devices you are using?
Not all USB devices need a Safe Removal. Things like Card Readers do not need the media ejected and can cause problems for the Root Hub for that specific device. You may check the Device Manager, look at the USB section and the Root Hubs. Some have a Reset option in the properties listing and if they do you might try hitting that button.