Since the original theme demo image doesn’t have any value in alt, I’m assuming there is a bug in the theme you might need to open a ticket for:
http://demo.woothemes.com/snapshot/
I don’t recommend altering original theme template functions but if you are very far into the project and rather not switch out to another theme, I can suggest few things you can try.
In admin-functions.php of the theme, I’d run var_dump($variable_name); where it relates to the function to see where exactly things get wrong. For example, maybe the thumbnail ID variable is null when trying to retrieve the alt text, and therefore returns the empty string. For example, $thumb_id is used as ID of where function grab the alt text:
if ($alt == '') $alt = esc_attr( get_post_meta($thumb_id, '_wp_attachment_image_alt', true) );
So you run var_dump($thumb_id); right before to see if it even holds the right value. If not, then you can trace where $thumb_id comes from and you can find:
$thumb_id = esc_html( get_post_meta($id,'_thumbnail_id',true) );
And you can var_dump($id); here to see if this one holds the right value. If not, then maybe this $id has been wrong since the beginning:
$id = $post->ID;
Then maybe you can try different method to get post ID such as
$id = get_the_ID();
I hope this will at least help you troubleshoot where the problem occurs in Snapshot and substitute the part with better code or point the problem out to WooThemes for faster support.