Vim: Difficulty setting up ctags. Source in subdirectories don't see tags file in project root

I'm trying to get setup with (exuberant) ctags on Vim today and am having difficulty getting it to work properly. I generate my ctags file on the command line with with:

cd myproj
ctags -R

This puts the tags file in myproj root. However, Vim only seems to read from this tags file when I'm working on source that reside in root. As I navigate to deeper directories, if I try to jump to a tag using <C-]>, I get:

E433: No tags file
E426: tag not found: MyClassName

I've verified that MyClassName does have a tag in the tags file, it's just that Vim doesn't see it. Can someone please explain how to configure Vim to reference the root's tags file?

Thanks.