It might be the link-checking time-out period is being exceeded, causing the plugin to mark the links as broken (?)
I have to be careful (I am sure others do as well…) about hogging too much server resources using Broken Link Checker (BLC) – I am using shared hosting; if too many server resources are being used I’ll start getting 500 errors, the database going away, etc. You have to experiment with the BLC advanced options to determine what server load setting works with your specific configuration. You might also want to ask your host to increase your allocated RAM… or possibly do it yourself in php.ini. Yes you will have to do some googling if none of this sounds like anything you are familiar with 😉
It so happens that the author of BLC also is the author of another very useful plugin, Error Log Monitor
http://w-shadow.com/blog/2012/07/25/error-log-monitor-plugin/ – maybe this might be useful to you as well?
