Many people have had this problem as the searchbox results will reveal. We have no control over the images Facebook selects to display. We have no control over how frequently they flush their images caches. The best advice we have is:
Only the first five images uploaded to a post (direct inclusion/gallery/slideshow) will be sent to Facebook. The images size has to be at least 200 x 200 pixels.
To select which image will be used for things like Facebook Publicize, you can use a theme that supports featured images. If a featured image isn’t set or your theme doesn’t use featured images, then the code tries to pick the first image in the post or page. If no image is found, then the blavatar is used.