What to do when a child says they can't, but you know they can?

This article (http://parenting.blogs.nytimes.com/2016/01/13/when-children-say-i-cant-but-they-can-and-adults-know-it/?WT_mc_id=2016-KWP-AUD_DEV?register=facebook) brought up a problem I face a lot, in response to this question…

Dearest Parenting Experts,

What advice do you
have for dealing with feigned incompetence in previously capable,
competent children? When a student suddenly regresses, claiming they
can’t complete skills I know they have mastered, or when a child
suddenly loses the ability to do the laundry,
say, flailing his boneless, ineffectual arms about as he jabs at
buttons on the washing machine, wailing all the while that he can’t
possibly do laundry; it’s too hard.

The article attempted to answer this, but honestly, while it did share some reasons kids do this, didn’t offer much practical advice on what’s a parent to
do. So, I thought I’d come here. Anyone have kids do this, and how do you handle it? Especially when you think it’s out of fear of failure (not just an act to get out of a job)…ie, when the tears and frustration seems real but you know that the task isn’t too hard or is even something the child’s previously shown he can do. Specific example and stories welcomed!