BPS takes over security and error handling to log events/errors in the Security Log file so yes it is possible that the root cause of this problem is something else and not BPS. Typically an intermittent problem indicates a cache, ISP connection or Host Server problem. If BPS is blocking something then it will be consistently blocked until you create a whitelist rule so it does not sound like the problem is being caused by BPS.
To completely eliminate BPS do these steps:
http://forum.ait-pro.com/forums/topic/read-me-first-free/#bps-free-general-troubleshooting
1. Make a backup of your .htaccess files first by going to the htaccess Core Backup & Restore tab page. Select the Backup htaccess Files Radio button and click the Backup Files button.
2. On the Security Modes page Activate Default Mode for the Root Folder BulletProof Mode.
3. On the Security Modes page select the Delete wp-admin .htaccess File Radio button and click the Activate button to deactivate/delete the wp-admin .htaccess file.