After prompting from Alicia, I investigated the comments issue.

MT sets the path on the cookie to the current directory. What this means is that if you are using permanent links, then the cookie will only remember you on an article by article basis.

This article explains a nice fix for the problem: Set the path to be /, and the domain to be your actual domain. I've done this, so hopefully you'll only have to enter your details one more time!