Video uploads brings up login prompt

When I try to upload videos, it takes me to the login screen as soon as the file finishes uploading (gets to the “Crunching” part). This is totally bizarre because I’m NOT logged out, and I’m able to upload images with no problem at all. I don’t get an error or anything, but the file never appears in my uploads folder or in my media library.

I’ve poked around various other threads here but couldn’t find anyone with this exact problem. I’ve updated my Flash but that didn’t help. Any ideas why this is happening?