After further testing I have some more info:
The problem is in the browser. If I use IE with a middle or higher privacy rating, it will not accept cookies from "third-party sites that do not have a compact privacy policy". Because my domain forwards to a path, it is considered a third-party site. I'm not sure how to influence my session variable's privacy policy in order to make it compact, but I will have to see.
Any thoughts?
Another possible solution would be to make my domain work correctly by not forwarding it but rather just having the domain work like all others, but I'm not sure that I know how to do that through my provider (http://www.thriftys.com). If anyone has gone through them before, I would very much appreciate any help you can offer. Thanks!