I tend to use sylpheed on Linux at home now when I need an off-line client.
My mother is in the same boat right now, and looking for suggestions. UTF-8 and prevalence of HTML content are making it nearly impossible to keep using in this day and age.
Best features (not killer but very nice) are/were the storage format, and saving attachments externally, and not "in line" with the message.
Local storage in an accessible format (Eudora uses mbox) is table stakes; roach motels need not apply.
I'm still running OS X 10.6 largely because of Eudora, but some day this machine will fail, or I'll have some compelling need to ‘upgrade’, and by then I'd like to have a better option than Eudora in a VM.
If you're open to new approaches to email you should try Unibox. It's an email client for Mac (and soon iOS) that lets you browse through your emails by person, so you always have all messages and all attachments with a person in one place.