How to encourage the unthankful...ignore them?
"How do you encourage her?" Excellent question. There are only two options: LIFE or DEATH.
First, make sure you don't assume that this person isn't ALREADY beating herself up over her own inability to have the right attitude. If a person has been made alive in Christ then in the inner man she desires the things of God. Plain and simple. This child of God, this joint-heir with Jesus is not TRYING to be unthankful, but is believing herself to be trapped by it!
IGNORING the inability (unthankfulness) is NOT what we have learned in Christ, but is what we learned from the world. The fact is that even when we scold a person for unthankfulness (I don't think you're suggesting that) we are ignoring the actual inability, and demanding that the person follow OUR method to appear thankful. We DID learn this one real good, didn't we? After all, many of us have been manipulated to say Thank you under the threat of losing something we wanted. The thankfulness that I will use against you will be that learned from the world stuff, and not the real McCoy. Real thankfulness hits us as miraculous. I think Bill Cosby gave us a good picture of our hypocrisy in his role where he says, "But we were THANKFUL!".
Thankfulness comes from the heart made alive by God. The law (or "good Christian principles") brings death; the Spirit brings life. The gospel (not the formula stuff) is what convinces us of this life of freedom. Preach it!!