Please edit your reply and delete all of the Security Log entries. I do not see anything unusual and just see standard log entries for things that should be blocked.
At this point I do not believe the problem is related to or being caused by the BPS plugin and have a feeling that the problem that has occurred is that your WordPress 4.5 upgrade installation did not complete fully/successfully. Do these steps below to manually upload new WordPress 4.5 folders and files to your website.
1. Download the WordPress 4.5 zip file here: https://www.ads-software.com/download/
2. Unzip the zip file on your computer.
3. Use FTP and connect to your website.
4. Upload all WordPress root files to your website root folder, Upload the entire wp-content folder, wp-includes folder and wp-admin folder to your website.
Note: doing these steps will ensure that your WordPress 4.5 installation is complete and will NOT overwrite any unique/specific files for your website. ie wp-config.php will not be overwritten. ie uploading the unzipped WordPress 4.5 wp-content folder will not overwrite your personal theme files or anything else in your wp-content folder like your personal plugins installed.