Hello Triangle Arts and Entertainment,
I don’t think updating will affect your customization, however I would advise you to make a back up of your site before updating, and make sure you know how to restore the site if you need to resort to that. You should create backups before updating anything.
Are you using WordPress menus feature to control your navigation? I would definitely recommend doing this if you haven’t switched to that method yet. It can really help solve problems like this and give you more control over your menus throughout your site.
Have you tried re-creating the categories after disabling the plugin to get your menus back?
Also, have you tried disabling all other plugins to see if that solve the issue?
Does this happen on the latest version of Twenty Eleven theme?
Since you’ve made customizations to the calendar files, have you ruled those out as possibly being the cause of this?
I hope this helps!