When I click on my handle to go to my uploads page, I get logged out. Every time. Is there something I should be doing differently?

You could find that your browser has the page (uploader) cached. Once you look at uploader if you go back into the forum does it still say your logged out?

I can't replicate your problem so fixing it if it's an actual error could be quite difficult.

Is anyone else experiencing this?

Yes, once it logs me out on uploader, I stay logged out on every page until I log back in.