The sorting options on Your Connections only work when the page is freshly loaded. That is, If I go to see my Connections, I can sort Following by A-Z, but if I switch from Following to Followers or Visitors, and then switch back to Following, the A-Z sort doesn't work. I have to click the Connections link at the left to instigate a fresh visit to the page for the A-Z sort to work.
The sort also doesn't work if you've gone to page 2 or used the jump.
In other words, the sort only works if it is the very first thing you do upon visiting the page. If any other action is performed, the sort no longer works.