The issue here is that there are 2 accesskey="s" values in separate forms. Both of these forms are roughly equally important to the page. Browsers handle duplicate access keys differently which leads to neither working as expected in some browser cases. Even removing one doesn't eliminate the issue because if you're in the other form, it still breaks. As such, the only approach that ends up making sense is to remove both of them from this page.
I'm not sure if this "fixes" the issue, but it can't happen any more; I've tagged this as "can't fix" to indicate that there's really a limited amount of things we can do with accesskeys in a situation like this page. Overriding the entire behavior of the browser accesskey stuff is not something we'd really be wanting to do (if we even could reliably, due to browser/OS variations).