I don't think the chain is ready to fail. The problem is when you run a chain beyond the recommended elongation, the chain will wear the chain rings and cassette and then when you put on a new chain, the new chain will quickly elongate.
I have heard that over the life of the ring gears and cogs that about 5 chains will be used up. So some people by 5 chains when they get new cogs and rings and rotate the chains on the bike so that they can get maximum life out of their systems. I have never done this. It also seems like the cheap chains that I use only last me about 500 miles of hill riding.