Hello James,
I am sorry for the delay of this reply.
I've checked your site and it seems like your site contain two username with the same alias-name (James-Helms). What happen is by default easysocial will use the alias-name as default permalink based on the setting here,
http://screen.stackideas.com/2015-03-02_1807.png and for some reason when user trying to edit the profile, the permalink value from the field does not following the permalink value from the database.
http://screen.stackideas.com/2015-03-02_1813.png
Regarding with the permalink not updated after saving is because by default the permalink format is following the permalink setting from the backend > easysocial > setting > user > Default user permalink format
http://screen.stackideas.com/2015-03-02_1807.png
The permalink actually does save and store correctly in the database but somehow the field is showing the permalink based on the setting mentioned above. However the permalink will displayed correctly when I turn the SEF on from your joomla backend.
I've applied the fix inside your \media\com_easysocial\apps\fields\user\permalink\permalink.php and it should display correctly now