When I was asked this question, I gave a smart a$$ reply.
I m not sure if they were impressed by the answer but it felt so.
My Strenght is " Try and Try till you succeed " . Then I gave them example of this site, how in the beginning it got only 10 views a day and today it gets millions.
My weakness is " Try and Try till you succeed ". I never give up even if it takes too long which is my weakness. Then I quote
"If at first you don't succeed, try, try again. Then quit. No use being a damn fool about it." - W.C. Fields
In this question you have to glorify yourself. The failure you mention should glorify what you do.
Saying that I m a workoholic as a failure will impress the panel in a job interview.
Hope you get the idea.