That's interesting. I don't use IE other than to check that websites work with it, but wouldn't expect more than one example to be running. I'd also expect it to disappear from task manager when shut down.
I don't know if it's meant to do that, but it may be the symptom of your problem. Trouble is, you can't uninstall and reinstall IE to fix it.
If you kill all those multiple copies, does it then work correctly next time?