Ok this is exactly what I expected to see. error_log is a default Server naming convention for a default/generic php error log file. This default error log is either being automatically created by your Host server or by a plugin. Since BPS Pro already comes with a php error log then you would not need to have/use an additional generic/default error_log file. Watch the video tutorial below, which has step by step instructions on how to exclude a single file (the generic error_log file) from being checked by AutoRestore.
How to exclude files or folders from being checked by ARQ. 99.99% of your website files are static files and typically only 2 to 5 dynamic files and folders will need to excluded from being checked by ARQ. How to exclude static files that are dynamically updated, how to exclude dynamic folders from being checked by ARQ and how to use the Quarantine Restore Files option.
http://forum.ait-pro.com/video-tutorials/#autorestore-quarantine