Things like this are stolen typically if there is a market for it. I bet that market is somewhere out of the country.
BBC reports the theft of two screen panels from Holy Trinity church in Torbryan, Devon. The church contains a marvelous medieval carved rood-screen, with panels showing paintings of saints. Two of these were hacked out of the screen by thieves last week.
Here is a link to the BBC story.
There is another story at the Independent.