Before you can find a solution to any problem you need to understand what the problem is.
http://httpd.apache.org/docs/current/mod/core.html#errordocument
http://httpd.apache.org/docs/2.2/mod/core.html#errordocument
The .htaccess ErrorDocument directive is a redirect directive that redirects Requests based on their HTTP response code to another URL. You can also display a message instead of redirecting to another URL.
BPS uses the ErrorDocument directive in the root .htaccess file to redirect 403 HTTP response codes to the BPS 403.php error logging template file. The 403.php error logging template file then logs the HTTP response code in your Security Log file.
Before assuming that any of these things below is the cause of the problem you need to check that you do not actually really have a redirect that is invalid that is redirecting back to itself and causing an infinite redirect loop. If you have redirect code that is redirecting back to the original URL then this will create in infinite redirect loop. Example: redirect X to X = infinite redirect loop. X is going to be either a full URL or a partial URL that is redirecting back to itself.
If your server does not allow the use of the ErrorDocument directive in an .htaccess file then either it will be ignored or an infinite redirect problem will occur and the error above will be displayed.
If you are using mod_security and mod_security is handling error logging an infinite redirect problem will occur and the error above will be displayed.
If something else you have installed on your website (another plugin or theme) is handling error logging an infinite redirect problem will occur and the error above will be displayed.
Normally when only BPS is handling error logging then a 403 HTTP response code will redirect to the 403.php error logging template, the 403 HTTP response code will be logged in your Security Log file and the process is complete per Request/HTTP response code. If something else on your website is also trying to redirect HTTP response codes then this creates in infinite redirect loop.
Solution: Either turn off error logging in whatever else you have installed on your website that is handling error logging or turn off BPS Security Log logging.