Second ajax button not working on user profile form
If Drupal can't find one of its core files it's nearly always because you're trying to use it in a context in which it wouldn't be automatically included.

For example when you use the user profile form normally, the menu item makes sure the file containing the form functions is included.

For your example the missing function is in user.pages.inc, so:

form_load_include($form_state, 'inc', 'user', 'user.pages');