I’ve checked your website, downloaded current logo and tried to upload it. I noticed that the maximum upload file size is set to 1kb.
To solve this, please add the following line to wp-config.php:
If the upload limit stays unchanged, create a file php.ini in your root folder (or if you have rights, edit etc/php.ini) and add/change the following lines:
memory_limit = 100M
file_uploads = On
upload_max_filesize = 100M
Have you tried setting WP_DEBUG to true in wp-config.php and see if there are some errors displayed when you save the theme options?