I just installed the plugin for the first time. It hung up and did not finish until, on the Advanced tab, I raised the Server load limit which was at 4.00 minutes and the note to the right indicated it had needed over 9 so I guess that's why it hung up (there are a lot of documents linked on the site as it is an investors' dataroom). I purposely put a broken link on the site to check the plugin and it had not found this broken link.
I raised the server load limit to 14.00 and within about 90 seconds it finished the job and correctly reported the broken link.
I am new at the plugin but I would think you could set the server load limit very low and then raise it when you want to run the check -- I am not saying that is necessary, only suggesting it for those who've had server crashing issues. It found the broken link just fine, and I need this plugin to keep track of all those documents so will limit the server load to just past what the plugin says is needed and also increase the time (number of hours -- on the General tab) between checks as the site's content isn't changed all that often.
You could also, depending on your needs, limit what the plugin checks on the "Looks for Links In" tab. I just put mine to published posts and pages, as I am not using the blogroll or comments.