Switching between visual & text editing loses image captions and positioning

My images are set up with captions. When I edit with the text editor, the captions seem to become just text following the images. I go back into the visual editor, edit the images and put the captions back on, and center the images. Save and look at the post, everything looks fine. Next time I have to use the text editor, the image caption turns back into text following the image and the image loses its centering, becoming left justified.

This is what the post looks like after using the text editor:
https://www.whetstone.wesley.edu/practice/2014/01/24/integrated-media-class-post/