I think you've mixed things a little bit. First of all, if the error states "A Question2Answer database query failed when generating this page." then the logs would should the SQL query that failed. So what you're seeing in the log is unrelated to the message you've pasted on top. It is unclear in your question how this could be linked to the open login plugin too.
Regarding the error you've found in the log, it has been generated after trying to use a file and PHP failed to read the file. That error would not allow Q2A to be properly loaded and would only display the white screen with a generic error. If the error is recurrent, then, it is likely that the file is not there. If the error is not often in the logs, then it is considerably likely that your hosting service is responsible for it. Maybe they were performing maintenance tasks on the server or whatever they do on them.