First, if you haven't already, there is an improved link check for admin...
http://www.dew-code.com/component/option,com_jooget/Itemid,27/task,detail/id,2/

It does not automate the task, but should work much better if your server has CURL installed (and most do these days)

I have developed a cronned (scheduled) link check routine, and did have some BETA testers testing it, but never got any feedback... Possibly that means it works perfectly.

I did plan to sell the add on for.. maybe $20 USD , but without feedback from
beta testers, I'm unable to ensure it works on various server environments.