I think Kovid's advice may only work if you also go into preferences -> Sending books to devices, and enable automatic metadata management.
What happens is that Calibre sends the epub along with the configured thumbnail, but when the Sony sees a new book it extracts the original/ugly cover. Enabling automatic metadata management will cause Calibre to overwrite the cover on the next connect. Since it's no longer a 'new' book the Sony will stop overwriting it.
Converting epub -> epub is a more permanent fix, but a bit more drastic. Probably best to use the Tweak epub feature and manually change out the image, but that does require a bit of knowledge about how epub works.