Since this plugin is simulating an RFI hacking method you will need to whitelist the argo-this.php file in the TimThumb / MISC File skip/bypass security filter. Add the argo-this.php file name to this security filter as shown below in your Root .htaccess file using the BPS built-in htaccess file editor.
Another issue/problem with this plugin that is not caused by or related to BPS would be if your web host is using mod_security and they have a SecRule or SecFilter that is blocking this plugin: See this WordPress Forum post: http://wordpress.org/support/topic/argo-links-403-error/page/2?replies=48
NOTE: The ait-pro.com domain is shown below in this security filter because this code example was taken from the ait-pro.com website. You will see your domain instead in this security filter.
# TIMTHUMB FORBID RFI and MISC FILE SKIP/BYPASS RULE
# Only Allow Internal File Requests From Your Website
# To Allow Additional Websites Access to a File Use [OR] as shown below.
# RewriteCond %{HTTP_REFERER} ^.*YourWebsite.com.* [OR]
# RewriteCond %{HTTP_REFERER} ^.*AnotherWebsite.com.*
RewriteCond %{QUERY_STRING} ^.*(http|https|ftp)(%3A|:)(%2F|/)(%2F|/)(w){0,3}.?(blogger|picasa|blogspot|tsunami|petapolitik|photobucket|imgur|imageshack|wordpress\.com|img\.youtube|tinypic\.com|upload\.wikimedia|kkc|start-thegame).*$ [NC,OR]
RewriteCond %{THE_REQUEST} ^.*(http|https|ftp)(%3A|:)(%2F|/)(%2F|/)(w){0,3}.?(blogger|picasa|blogspot|tsunami|petapolitik|photobucket|imgur|imageshack|wordpress\.com|img\.youtube|tinypic\.com|upload\.wikimedia|kkc|start-thegame).*$ [NC]
RewriteRule .* index.php [F,L]
RewriteCond %{REQUEST_URI} (argo-this\.php|timthumb\.php|phpthumb\.php|thumb\.php|thumbs\.php) [NC]
RewriteCond %{HTTP_REFERER} ^.*ait-pro.com.*
RewriteRule . - [S=1]