Before checking folder permissions, try to update BPS Pro a couple of times. I believe I have seen this error before once and it just had to do with a server hiccup at the time the update was tried. The update worked on the second update try.
This WordPress error usually means that your folder permissions are set too restrictive for either the /wp-content/ folder and/or the /wp-content/plugins/ folder. If you can still view the BPS Pro System Info page then go to the BPS Pro System Info page and check your folder permissions for these folders: /wp-content/ and /wp-content/plugins/ folders. Also check all of your other website folders for any folder permission problems. Folder permissions should be either 755 or 705 (some web hosts do not allow 705 folder permissions). Also check file permissions. File permissions should be either 644 or 604 (depends on the type of server you have). Also check that the Script Owner User ID (UID) and File Owner User ID match for all of your website folders in the BPS Pro System Info File|Folder Permissions Table. If you are unable to view the BPS Pro System Info page then you will need to use your web host control panel file manager or FTP to view folder permissions and folder Ownership.