I've sort of been in your situation while working for another employer.
Is there a way to come along side the person and help them see how to boost their performance permanently? And at the same time explain that this is maybe a bigger deal than they're thinking. None of is guaranteed a job and even in the current job market (sort of tight in my area), jobs that start at $15 aren't that plentiful.
As far as being performanced out, and I'm not sure this is still true, but I was told a long while back that a TM would be coached 3 times for the same issue before being terminated for it (assuming it's not theft or something equally egregious). Has this TM been formally coached yet? Maybe that would help shake up their thinking and push them to do better.
