Thanks balinor, but it didn't change anything.
I added the following code to the ui_tabs.tpl file and the tab still shows up even if the extra fields are blank.
Code:
{* Extra Fields Tab Content *}
{if $active_modules.Extra_Fields}
{foreach from=$extra_fields item=v}
{if $v.active eq "Y" and $v.field_value}
<div id="product-tabs-{$v.field|replace:" ":"-"}">
{$v.field_value}
</div>
{/if}
{/foreach}
{/if}
{* End Extra Fields Tab Content *}